diff --git a/icu4c/source/i18n/number_formatimpl.cpp b/icu4c/source/i18n/number_formatimpl.cpp
index 8127dd892a7..be0b7c8014d 100644
--- a/icu4c/source/i18n/number_formatimpl.cpp
+++ b/icu4c/source/i18n/number_formatimpl.cpp
@@ -111,7 +111,6 @@ void NumberFormatterImpl::preProcess(DecimalQuantity& inValue, MicroProps& micro
         return;
     }
     fMicroPropsGenerator->processQuantity(inValue, microsOut, status);
-    microsOut.rounder.apply(inValue, status);
     microsOut.integerWidth.apply(inValue, status);
 }
 
@@ -124,7 +123,6 @@ MicroProps& NumberFormatterImpl::preProcessUnsafe(DecimalQuantity& inValue, UErr
         return fMicros; // must always return a value
     }
     fMicroPropsGenerator->processQuantity(inValue, fMicros, status);
-    fMicros.rounder.apply(inValue, status);
     fMicros.integerWidth.apply(inValue, status);
     return fMicros;
 }
diff --git a/icu4c/source/i18n/number_patternmodifier.cpp b/icu4c/source/i18n/number_patternmodifier.cpp
index 10b20c6a49e..892ac372f51 100644
--- a/icu4c/source/i18n/number_patternmodifier.cpp
+++ b/icu4c/source/i18n/number_patternmodifier.cpp
@@ -124,6 +124,7 @@ ImmutablePatternModifier::ImmutablePatternModifier(AdoptingModifierStore* pm, co
 void ImmutablePatternModifier::processQuantity(DecimalQuantity& quantity, MicroProps& micros,
                                                UErrorCode& status) const {
     parent->processQuantity(quantity, micros, status);
+    micros.rounder.apply(quantity, status);
     if (micros.modMiddle != nullptr) {
         return;
     }
@@ -162,6 +163,7 @@ MicroPropsGenerator& MutablePatternModifier::addToChain(const MicroPropsGenerato
 void MutablePatternModifier::processQuantity(DecimalQuantity& fq, MicroProps& micros,
                                              UErrorCode& status) const {
     fParent->processQuantity(fq, micros, status);
+    micros.rounder.apply(fq, status);
     if (micros.modMiddle != nullptr) {
         return;
     }
diff --git a/icu4c/source/i18n/unicode/unumberformatter.h b/icu4c/source/i18n/unicode/unumberformatter.h
index b27507f7a8f..1d6b46030d0 100644
--- a/icu4c/source/i18n/unicode/unumberformatter.h
+++ b/icu4c/source/i18n/unicode/unumberformatter.h
@@ -336,7 +336,7 @@ typedef enum UNumberSignDisplay {
 
     /**
      * Show the minus sign on negative numbers and the plus sign on positive numbers. Do not show a
-     * sign on zero or NaN, unless the sign bit is set (-0.0 gets a sign).
+     * sign on zero, numbers that round to zero, or NaN.
      *
      * @stable ICU 61
      */
@@ -344,9 +344,8 @@ typedef enum UNumberSignDisplay {
 
     /**
      * Use the locale-dependent accounting format on negative numbers, and show the plus sign on
-     * positive numbers. Do not show a sign on zero or NaN, unless the sign bit is set (-0.0 gets a
-     * sign). For more information on the accounting format, see the ACCOUNTING sign display
-     * strategy.
+     * positive numbers. Do not show a sign on zero, numbers that round to zero, or NaN. For more
+     * information on the accounting format, see the ACCOUNTING sign display strategy.
      *
      * @stable ICU 61
      */
diff --git a/icu4c/source/test/intltest/numbertest.h b/icu4c/source/test/intltest/numbertest.h
index 7f5bcdf4a8e..adccc9e7755 100644
--- a/icu4c/source/test/intltest/numbertest.h
+++ b/icu4c/source/test/intltest/numbertest.h
@@ -68,6 +68,7 @@ class NumberFormatterApiTest : public IntlTestWithFieldPosition {
     // TODO: Add this method if currency symbols override support is added.
     //void symbolsOverride();
     void sign();
+    void signNearZero();
     void signCoverage();
     void decimal();
     void scale();
diff --git a/icu4c/source/test/intltest/numbertest_api.cpp b/icu4c/source/test/intltest/numbertest_api.cpp
index 726e7c5ce48..8d82acd076f 100644
--- a/icu4c/source/test/intltest/numbertest_api.cpp
+++ b/icu4c/source/test/intltest/numbertest_api.cpp
@@ -86,6 +86,7 @@ void NumberFormatterApiTest::runIndexedTest(int32_t index, UBool exec, const cha
         // TODO: Add this method if currency symbols override support is added.
         //TESTCASE_AUTO(symbolsOverride);
         TESTCASE_AUTO(sign);
+        TESTCASE_AUTO(signNearZero);
         TESTCASE_AUTO(signCoverage);
         TESTCASE_AUTO(decimal);
         TESTCASE_AUTO(scale);
@@ -1694,6 +1695,57 @@ void NumberFormatterApiTest::integerWidth() {
             u"00.008765",
             u"00");
 
+    assertFormatDescending(
+            u"Integer Width Compact",
+            u"compact-short integer-width/000",
+            NumberFormatter::with()
+                .notation(Notation::compactShort())
+                .integerWidth(IntegerWidth::zeroFillTo(3).truncateAt(3)),
+            Locale::getEnglish(),
+            u"088K",
+            u"008.8K",
+            u"876",
+            u"088",
+            u"008.8",
+            u"000.88",
+            u"000.088",
+            u"000.0088",
+            u"000");
+
+    assertFormatDescending(
+            u"Integer Width Scientific",
+            u"scientific integer-width/000",
+            NumberFormatter::with()
+                .notation(Notation::scientific())
+                .integerWidth(IntegerWidth::zeroFillTo(3).truncateAt(3)),
+            Locale::getEnglish(),
+            u"008.765E4",
+            u"008.765E3",
+            u"008.765E2",
+            u"008.765E1",
+            u"008.765E0",
+            u"008.765E-1",
+            u"008.765E-2",
+            u"008.765E-3",
+            u"000E0");
+
+    assertFormatDescending(
+            u"Integer Width Engineering",
+            u"engineering integer-width/000",
+            NumberFormatter::with()
+                .notation(Notation::engineering())
+                .integerWidth(IntegerWidth::zeroFillTo(3).truncateAt(3)),
+            Locale::getEnglish(),
+            u"087.65E3",
+            u"008.765E3",
+            u"876.5E0",
+            u"087.65E0",
+            u"008.765E0",
+            u"876.5E-3",
+            u"087.65E-3",
+            u"008.765E-3",
+            u"000E0");
+
     assertFormatSingle(
             u"Integer Width Remove All A",
             u"integer-width/00",
@@ -2104,6 +2156,49 @@ void NumberFormatterApiTest::sign() {
             u"-444,444.00 US dollars");
 }
 
+void NumberFormatterApiTest::signNearZero() {
+    // https://unicode-org.atlassian.net/browse/ICU-20709
+    IcuTestErrorCode status(*this, "signNearZero");
+    const struct TestCase {
+        UNumberSignDisplay sign;
+        double input;
+        const char16_t* expected;
+    } cases[] = {
+        { UNUM_SIGN_AUTO,  1.1, u"1" },
+        { UNUM_SIGN_AUTO,  0.9, u"1" },
+        { UNUM_SIGN_AUTO,  0.1, u"0" },
+        { UNUM_SIGN_AUTO, -0.1, u"-0" }, // interesting case
+        { UNUM_SIGN_AUTO, -0.9, u"-1" },
+        { UNUM_SIGN_AUTO, -1.1, u"-1" },
+        { UNUM_SIGN_ALWAYS,  1.1, u"+1" },
+        { UNUM_SIGN_ALWAYS,  0.9, u"+1" },
+        { UNUM_SIGN_ALWAYS,  0.1, u"+0" },
+        { UNUM_SIGN_ALWAYS, -0.1, u"-0" },
+        { UNUM_SIGN_ALWAYS, -0.9, u"-1" },
+        { UNUM_SIGN_ALWAYS, -1.1, u"-1" },
+        { UNUM_SIGN_EXCEPT_ZERO,  1.1, u"+1" },
+        { UNUM_SIGN_EXCEPT_ZERO,  0.9, u"+1" },
+        { UNUM_SIGN_EXCEPT_ZERO,  0.1, u"0" }, // interesting case
+        { UNUM_SIGN_EXCEPT_ZERO, -0.1, u"0" }, // interesting case
+        { UNUM_SIGN_EXCEPT_ZERO, -0.9, u"-1" },
+        { UNUM_SIGN_EXCEPT_ZERO, -1.1, u"-1" },
+    };
+    for (auto& cas : cases) {
+        auto sign = cas.sign;
+        auto input = cas.input;
+        auto expected = cas.expected;
+        auto actual = NumberFormatter::with()
+            .sign(sign)
+            .precision(Precision::integer())
+            .locale(Locale::getUS())
+            .formatDouble(input, status)
+            .toString(status);
+        assertEquals(
+            DoubleToUnicodeString(input) + " @ SignDisplay " + Int64ToUnicodeString(sign),
+            expected, actual);
+    }
+}
+
 void NumberFormatterApiTest::signCoverage() {
     // https://unicode-org.atlassian.net/browse/ICU-20708
     IcuTestErrorCode status(*this, "signCoverage");
diff --git a/icu4c/source/test/testdata/numberpermutationtest.txt b/icu4c/source/test/testdata/numberpermutationtest.txt
index b9c8558d1e6..4b4656e8b0a 100644
--- a/icu4c/source/test/testdata/numberpermutationtest.txt
+++ b/icu4c/source/test/testdata/numberpermutationtest.txt
@@ -2273,15 +2273,15 @@ compact-short precision-integer sign-accounting-except-zero
   es-MX
     0
     +92 k
-    -0
+    0
   zh-TW
     0
     +9萬
-    -0
+    0
   bn-BD
     ০
     +৯২ হা
-    -০
+    ০
 
 compact-short .000 sign-accounting-except-zero
   es-MX
@@ -4849,15 +4849,15 @@ percent precision-integer sign-accounting-except-zero
   es-MX
     0 %
     +91,827 %
-    -0 %
+    0 %
   zh-TW
     0%
     +91,827%
-    -0%
+    0%
   bn-BD
     ০%
     +৯১,৮২৭%
-    -০%
+    ০%
 
 percent .000 sign-accounting-except-zero
   es-MX
@@ -4905,15 +4905,15 @@ currency/EUR precision-integer sign-accounting-except-zero
   es-MX
     EUR 0
     +EUR 91,827
-    -EUR 0
+    EUR 0
   zh-TW
     €0
     +€91,827
-    (€0)
+    €0
   bn-BD
     ০€
     +৯১,৮২৭€
-    (০ €)
+    ০€
 
 currency/EUR .000 sign-accounting-except-zero
   es-MX
@@ -4961,15 +4961,15 @@ measure-unit/length-furlong precision-integer sign-accounting-except-zero
   es-MX
     0 fur
     +91,827 fur
-    -0 fur
+    0 fur
   zh-TW
     0 化朗
     +91,827 化朗
-    -0 化朗
+    0 化朗
   bn-BD
     ০ ফার্লং
     +৯১,৮২৭ ফার্লং
-    -০ ফার্লং
+    ০ ফার্লং
 
 measure-unit/length-furlong .000 sign-accounting-except-zero
   es-MX
@@ -6627,15 +6627,15 @@ unit-width-narrow precision-integer sign-accounting-except-zero
   es-MX
     0
     +91,827
-    -0
+    0
   zh-TW
     0
     +91,827
-    -0
+    0
   bn-BD
     ০
     +৯১,৮২৭
-    -০
+    ০
 
 unit-width-narrow .000 sign-accounting-except-zero
   es-MX
@@ -6683,15 +6683,15 @@ unit-width-full-name precision-integer sign-accounting-except-zero
   es-MX
     0
     +91,827
-    -0
+    0
   zh-TW
     0
     +91,827
-    -0
+    0
   bn-BD
     ০
     +৯১,৮২৭
-    -০
+    ০
 
 unit-width-full-name .000 sign-accounting-except-zero
   es-MX
@@ -7943,15 +7943,15 @@ precision-integer integer-width/##00 sign-accounting-except-zero
   es-MX
     00
     +1827
-    -00
+    00
   zh-TW
     00
     +1,827
-    -00
+    00
   bn-BD
     ০০
     +১,৮২৭
-    -০০
+    ০০
 
 .000 integer-width/##00 sign-accounting-except-zero
   es-MX
@@ -8167,15 +8167,15 @@ precision-integer scale/0.5 sign-accounting-except-zero
   es-MX
     0
     +45,914
-    -0
+    0
   zh-TW
     0
     +45,914
-    -0
+    0
   bn-BD
     ০
     +৪৫,৯১৪
-    -০
+    ০
 
 .000 scale/0.5 sign-accounting-except-zero
   es-MX
@@ -8335,15 +8335,15 @@ precision-integer group-on-aligned sign-accounting-except-zero
   es-MX
     0
     +91,827
-    -0
+    0
   zh-TW
     0
     +91,827
-    -0
+    0
   bn-BD
     ০
     +৯১,৮২৭
-    -০
+    ০
 
 .000 group-on-aligned sign-accounting-except-zero
   es-MX
@@ -8447,15 +8447,15 @@ precision-integer latin sign-accounting-except-zero
   es-MX
     0
     +91,827
-    -0
+    0
   zh-TW
     0
     +91,827
-    -0
+    0
   bn-BD
     0
     +91,827
-    -0
+    0
 
 .000 latin sign-accounting-except-zero
   es-MX
@@ -8559,15 +8559,15 @@ precision-integer sign-accounting-except-zero decimal-always
   es-MX
     0.
     +91,827.
-    -0.
+    0.
   zh-TW
     0.
     +91,827.
-    -0.
+    0.
   bn-BD
     ০.
     +৯১,৮২৭.
-    -০.
+    ০.
 
 .000 sign-accounting-except-zero decimal-always
   es-MX
diff --git a/icu4j/main/classes/core/src/com/ibm/icu/impl/number/MutablePatternModifier.java b/icu4j/main/classes/core/src/com/ibm/icu/impl/number/MutablePatternModifier.java
index 8dad5fcfba1..2a441513ab4 100644
--- a/icu4j/main/classes/core/src/com/ibm/icu/impl/number/MutablePatternModifier.java
+++ b/icu4j/main/classes/core/src/com/ibm/icu/impl/number/MutablePatternModifier.java
@@ -231,6 +231,9 @@ public class MutablePatternModifier implements Modifier, SymbolProvider, MicroPr
         @Override
         public MicroProps processQuantity(DecimalQuantity quantity) {
             MicroProps micros = parent.processQuantity(quantity);
+            if (micros.rounder != null) {
+                micros.rounder.apply(quantity);
+            }
             if (micros.modMiddle != null) {
                 return micros;
             }
@@ -268,6 +271,9 @@ public class MutablePatternModifier implements Modifier, SymbolProvider, MicroPr
     @Override
     public MicroProps processQuantity(DecimalQuantity fq) {
         MicroProps micros = parent.processQuantity(fq);
+        if (micros.rounder != null) {
+            micros.rounder.apply(fq);
+        }
         if (micros.modMiddle != null) {
             return micros;
         }
diff --git a/icu4j/main/classes/core/src/com/ibm/icu/number/NumberFormatter.java b/icu4j/main/classes/core/src/com/ibm/icu/number/NumberFormatter.java
index 497800e3b03..ff0a0a017b0 100644
--- a/icu4j/main/classes/core/src/com/ibm/icu/number/NumberFormatter.java
+++ b/icu4j/main/classes/core/src/com/ibm/icu/number/NumberFormatter.java
@@ -327,7 +327,7 @@ public final class NumberFormatter {
 
         /**
          * Show the minus sign on negative numbers and the plus sign on positive numbers. Do not show a
-         * sign on zero or NaN, unless the sign bit is set (-0.0 gets a sign).
+         * sign on zero, numbers that round to zero, or NaN.
          *
          * @stable ICU 61
          * @see NumberFormatter
@@ -336,9 +336,8 @@ public final class NumberFormatter {
 
         /**
          * Use the locale-dependent accounting format on negative numbers, and show the plus sign on
-         * positive numbers. Do not show a sign on zero or NaN, unless the sign bit is set (-0.0 gets a
-         * sign). For more information on the accounting format, see the ACCOUNTING sign display
-         * strategy.
+         * positive numbers. Do not show a sign on zero, numbers that round to zero, or NaN. For more
+         * information on the accounting format, see the ACCOUNTING sign display strategy.
          *
          * @stable ICU 61
          * @see NumberFormatter
diff --git a/icu4j/main/classes/core/src/com/ibm/icu/number/NumberFormatterImpl.java b/icu4j/main/classes/core/src/com/ibm/icu/number/NumberFormatterImpl.java
index 208c02a93db..48607c051a6 100644
--- a/icu4j/main/classes/core/src/com/ibm/icu/number/NumberFormatterImpl.java
+++ b/icu4j/main/classes/core/src/com/ibm/icu/number/NumberFormatterImpl.java
@@ -98,9 +98,6 @@ class NumberFormatterImpl {
      */
     public MicroProps preProcess(DecimalQuantity inValue) {
         MicroProps micros = microPropsGenerator.processQuantity(inValue);
-        if (micros.rounder != null) {
-            micros.rounder.apply(inValue);
-        }
         if (micros.integerWidth.maxInt == -1) {
             inValue.setMinInteger(micros.integerWidth.minInt);
         } else {
@@ -114,9 +111,6 @@ class NumberFormatterImpl {
         MicroProps micros = new MicroProps(false);
         MicroPropsGenerator microPropsGenerator = macrosToMicroGenerator(macros, micros, false);
         micros = microPropsGenerator.processQuantity(inValue);
-        if (micros.rounder != null) {
-            micros.rounder.apply(inValue);
-        }
         if (micros.integerWidth.maxInt == -1) {
             inValue.setMinInteger(micros.integerWidth.minInt);
         } else {
diff --git a/icu4j/main/tests/core/src/com/ibm/icu/dev/data/numberpermutationtest.txt b/icu4j/main/tests/core/src/com/ibm/icu/dev/data/numberpermutationtest.txt
index 25f7da8b7bb..4b4656e8b0a 100644
--- a/icu4j/main/tests/core/src/com/ibm/icu/dev/data/numberpermutationtest.txt
+++ b/icu4j/main/tests/core/src/com/ibm/icu/dev/data/numberpermutationtest.txt
@@ -1,4 +1,4 @@
-# © 2017 and later: Unicode, Inc. and others.
+# © 2019 and later: Unicode, Inc. and others.
 # License & terms of use: http://www.unicode.org/copyright.html
 
 compact-short percent unit-width-narrow
@@ -2273,15 +2273,15 @@ compact-short precision-integer sign-accounting-except-zero
   es-MX
     0
     +92 k
-    -0
+    0
   zh-TW
     0
     +9萬
-    -0
+    0
   bn-BD
     ০
     +৯২ হা
-    -০
+    ০
 
 compact-short .000 sign-accounting-except-zero
   es-MX
@@ -4849,15 +4849,15 @@ percent precision-integer sign-accounting-except-zero
   es-MX
     0 %
     +91,827 %
-    -0 %
+    0 %
   zh-TW
     0%
     +91,827%
-    -0%
+    0%
   bn-BD
     ০%
     +৯১,৮২৭%
-    -০%
+    ০%
 
 percent .000 sign-accounting-except-zero
   es-MX
@@ -4905,15 +4905,15 @@ currency/EUR precision-integer sign-accounting-except-zero
   es-MX
     EUR 0
     +EUR 91,827
-    -EUR 0
+    EUR 0
   zh-TW
     €0
     +€91,827
-    (€0)
+    €0
   bn-BD
     ০€
     +৯১,৮২৭€
-    (০ €)
+    ০€
 
 currency/EUR .000 sign-accounting-except-zero
   es-MX
@@ -4961,15 +4961,15 @@ measure-unit/length-furlong precision-integer sign-accounting-except-zero
   es-MX
     0 fur
     +91,827 fur
-    -0 fur
+    0 fur
   zh-TW
     0 化朗
     +91,827 化朗
-    -0 化朗
+    0 化朗
   bn-BD
     ০ ফার্লং
     +৯১,৮২৭ ফার্লং
-    -০ ফার্লং
+    ০ ফার্লং
 
 measure-unit/length-furlong .000 sign-accounting-except-zero
   es-MX
@@ -6627,15 +6627,15 @@ unit-width-narrow precision-integer sign-accounting-except-zero
   es-MX
     0
     +91,827
-    -0
+    0
   zh-TW
     0
     +91,827
-    -0
+    0
   bn-BD
     ০
     +৯১,৮২৭
-    -০
+    ০
 
 unit-width-narrow .000 sign-accounting-except-zero
   es-MX
@@ -6683,15 +6683,15 @@ unit-width-full-name precision-integer sign-accounting-except-zero
   es-MX
     0
     +91,827
-    -0
+    0
   zh-TW
     0
     +91,827
-    -0
+    0
   bn-BD
     ০
     +৯১,৮২৭
-    -০
+    ০
 
 unit-width-full-name .000 sign-accounting-except-zero
   es-MX
@@ -7943,15 +7943,15 @@ precision-integer integer-width/##00 sign-accounting-except-zero
   es-MX
     00
     +1827
-    -00
+    00
   zh-TW
     00
     +1,827
-    -00
+    00
   bn-BD
     ০০
     +১,৮২৭
-    -০০
+    ০০
 
 .000 integer-width/##00 sign-accounting-except-zero
   es-MX
@@ -8167,15 +8167,15 @@ precision-integer scale/0.5 sign-accounting-except-zero
   es-MX
     0
     +45,914
-    -0
+    0
   zh-TW
     0
     +45,914
-    -0
+    0
   bn-BD
     ০
     +৪৫,৯১৪
-    -০
+    ০
 
 .000 scale/0.5 sign-accounting-except-zero
   es-MX
@@ -8335,15 +8335,15 @@ precision-integer group-on-aligned sign-accounting-except-zero
   es-MX
     0
     +91,827
-    -0
+    0
   zh-TW
     0
     +91,827
-    -0
+    0
   bn-BD
     ০
     +৯১,৮২৭
-    -০
+    ০
 
 .000 group-on-aligned sign-accounting-except-zero
   es-MX
@@ -8447,15 +8447,15 @@ precision-integer latin sign-accounting-except-zero
   es-MX
     0
     +91,827
-    -0
+    0
   zh-TW
     0
     +91,827
-    -0
+    0
   bn-BD
     0
     +91,827
-    -0
+    0
 
 .000 latin sign-accounting-except-zero
   es-MX
@@ -8559,15 +8559,15 @@ precision-integer sign-accounting-except-zero decimal-always
   es-MX
     0.
     +91,827.
-    -0.
+    0.
   zh-TW
     0.
     +91,827.
-    -0.
+    0.
   bn-BD
     ০.
     +৯১,৮২৭.
-    -০.
+    ০.
 
 .000 sign-accounting-except-zero decimal-always
   es-MX
diff --git a/icu4j/main/tests/core/src/com/ibm/icu/dev/test/number/NumberFormatterApiTest.java b/icu4j/main/tests/core/src/com/ibm/icu/dev/test/number/NumberFormatterApiTest.java
index dbbf4646826..a12468f2c19 100644
--- a/icu4j/main/tests/core/src/com/ibm/icu/dev/test/number/NumberFormatterApiTest.java
+++ b/icu4j/main/tests/core/src/com/ibm/icu/dev/test/number/NumberFormatterApiTest.java
@@ -1625,6 +1625,57 @@ public class NumberFormatterApiTest {
                 "00.008765",
                 "00");
 
+        assertFormatDescending(
+                "Integer Width Compact",
+                "compact-short integer-width/000",
+                NumberFormatter.with()
+                    .notation(Notation.compactShort())
+                    .integerWidth(IntegerWidth.zeroFillTo(3).truncateAt(3)),
+                ULocale.ENGLISH,
+                "088K",
+                "008.8K",
+                "876",
+                "088",
+                "008.8",
+                "000.88",
+                "000.088",
+                "000.0088",
+                "000");
+
+        assertFormatDescending(
+                "Integer Width Scientific",
+                "scientific integer-width/000",
+                NumberFormatter.with()
+                    .notation(Notation.scientific())
+                    .integerWidth(IntegerWidth.zeroFillTo(3).truncateAt(3)),
+                ULocale.ENGLISH,
+                "008.765E4",
+                "008.765E3",
+                "008.765E2",
+                "008.765E1",
+                "008.765E0",
+                "008.765E-1",
+                "008.765E-2",
+                "008.765E-3",
+                "000E0");
+
+        assertFormatDescending(
+                "Integer Width Engineering",
+                "engineering integer-width/000",
+                NumberFormatter.with()
+                    .notation(Notation.engineering())
+                    .integerWidth(IntegerWidth.zeroFillTo(3).truncateAt(3)),
+                ULocale.ENGLISH,
+                "087.65E3",
+                "008.765E3",
+                "876.5E0",
+                "087.65E0",
+                "008.765E0",
+                "876.5E-3",
+                "087.65E-3",
+                "008.765E-3",
+                "000E0");
+
         assertFormatSingle(
                 "Integer Width Remove All A",
                 "integer-width/00",
@@ -2029,6 +2080,45 @@ public class NumberFormatterApiTest {
                 "-444,444.00 US dollars");
     }
 
+    @Test
+    public void signNearZero() {
+        // https://unicode-org.atlassian.net/browse/ICU-20709
+        Object[][] cases = {
+            { SignDisplay.AUTO,  1.1, "1" },
+            { SignDisplay.AUTO,  0.9, "1" },
+            { SignDisplay.AUTO,  0.1, "0" },
+            { SignDisplay.AUTO, -0.1, "-0" }, // interesting case
+            { SignDisplay.AUTO, -0.9, "-1" },
+            { SignDisplay.AUTO, -1.1, "-1" },
+            { SignDisplay.ALWAYS,  1.1, "+1" },
+            { SignDisplay.ALWAYS,  0.9, "+1" },
+            { SignDisplay.ALWAYS,  0.1, "+0" },
+            { SignDisplay.ALWAYS, -0.1, "-0" },
+            { SignDisplay.ALWAYS, -0.9, "-1" },
+            { SignDisplay.ALWAYS, -1.1, "-1" },
+            { SignDisplay.EXCEPT_ZERO,  1.1, "+1" },
+            { SignDisplay.EXCEPT_ZERO,  0.9, "+1" },
+            { SignDisplay.EXCEPT_ZERO,  0.1, "0" }, // interesting case
+            { SignDisplay.EXCEPT_ZERO, -0.1, "0" }, // interesting case
+            { SignDisplay.EXCEPT_ZERO, -0.9, "-1" },
+            { SignDisplay.EXCEPT_ZERO, -1.1, "-1" },
+        };
+        for (Object[] cas : cases) {
+            SignDisplay sign = (SignDisplay) cas[0];
+            double input = (Double) cas[1];
+            String expected = (String) cas[2];
+            String actual = NumberFormatter.with()
+                .sign(sign)
+                .precision(Precision.integer())
+                .locale(Locale.US)
+                .format(input)
+                .toString();
+            assertEquals(
+                input + " @ SignDisplay " + sign,
+                expected, actual);
+        }
+    }
+
     @Test
     public void signCoverage() {
         // https://unicode-org.atlassian.net/browse/ICU-20708
diff --git a/icu4j/main/tests/core/src/com/ibm/icu/dev/test/number/NumberPermutationTest.java b/icu4j/main/tests/core/src/com/ibm/icu/dev/test/number/NumberPermutationTest.java
index 3ce326fa313..d7056b9c7a5 100644
--- a/icu4j/main/tests/core/src/com/ibm/icu/dev/test/number/NumberPermutationTest.java
+++ b/icu4j/main/tests/core/src/com/ibm/icu/dev/test/number/NumberPermutationTest.java
@@ -96,7 +96,7 @@ public class NumberPermutationTest extends TestFmwk {
 
         // Build up the golden data string as we evaluate all permutations
         ArrayList<String> resultLines = new ArrayList<>();
-        resultLines.add("# © 2017 and later: Unicode, Inc. and others.");
+        resultLines.add("# © 2019 and later: Unicode, Inc. and others.");
         resultLines.add("# License & terms of use: http://www.unicode.org/copyright.html");
         resultLines.add("");