diff --git a/icu4c/source/common/locid.cpp b/icu4c/source/common/locid.cpp
index 4fec17d14fd..02cd82a7b8e 100644
--- a/icu4c/source/common/locid.cpp
+++ b/icu4c/source/common/locid.cpp
@@ -2515,16 +2515,16 @@ public:
 
     virtual const char* next(int32_t* resultLength, UErrorCode& status) {
         const char* legacy_key = KeywordEnumeration::next(nullptr, status);
-        if (U_SUCCESS(status) && legacy_key != nullptr) {
+        while (U_SUCCESS(status) && legacy_key != nullptr) {
             const char* key = uloc_toUnicodeLocaleKey(legacy_key);
-            if (key == nullptr) {
-                status = U_ILLEGAL_ARGUMENT_ERROR;
-            } else {
+            if (key != nullptr) {
                 if (resultLength != nullptr) {
                     *resultLength = static_cast<int32_t>(uprv_strlen(key));
                 }
                 return key;
             }
+            // Not a Unicode keyword, could be a t, x or other, continue to look at the next one.
+            legacy_key = KeywordEnumeration::next(nullptr, status);
         }
         if (resultLength != nullptr) *resultLength = 0;
         return nullptr;
diff --git a/icu4c/source/test/intltest/loctest.cpp b/icu4c/source/test/intltest/loctest.cpp
index 53d5721a98f..ce41a4c00e7 100644
--- a/icu4c/source/test/intltest/loctest.cpp
+++ b/icu4c/source/test/intltest/loctest.cpp
@@ -239,8 +239,10 @@ void LocaleTest::runIndexedTest( int32_t index, UBool exec, const char* &name, c
     TESTCASE_AUTO(TestKeywordVariantParsing);
     TESTCASE_AUTO(TestCreateKeywordSet);
     TESTCASE_AUTO(TestCreateKeywordSetEmpty);
+    TESTCASE_AUTO(TestCreateKeywordSetWithPrivateUse);
     TESTCASE_AUTO(TestCreateUnicodeKeywordSet);
     TESTCASE_AUTO(TestCreateUnicodeKeywordSetEmpty);
+    TESTCASE_AUTO(TestCreateUnicodeKeywordSetWithPrivateUse);
     TESTCASE_AUTO(TestGetKeywordValueStdString);
     TESTCASE_AUTO(TestGetUnicodeKeywordValueStdString);
     TESTCASE_AUTO(TestSetKeywordValue);
@@ -4084,6 +4086,27 @@ LocaleTest::TestCreateKeywordSetEmpty(void) {
     assertEquals("set::size()", 0, static_cast<int32_t>(result.size()));
 }
 
+void
+LocaleTest::TestCreateKeywordSetWithPrivateUse(void) {
+    IcuTestErrorCode status(*this, "TestCreateKeywordSetWithPrivateUse()");
+
+    static const char tag[] = "en-US-u-ca-gregory-x-foo";
+    static const Locale l = Locale::forLanguageTag(tag, status);
+    std::set<std::string> result;
+    l.getKeywords<std::string>(
+                 std::insert_iterator<decltype(result)>(result, result.begin()),
+            status);
+    status.errIfFailureAndReset("getKeywords \"%s\"", l.getName());
+    assertTrue("getKeywords set::find(\"calendar\")",
+               result.find("calendar") != result.end());
+    assertTrue("getKeywords set::find(\"ca\")",
+               result.find("ca") == result.end());
+    assertTrue("getKeywords set::find(\"x\")",
+               result.find("x") != result.end());
+    assertTrue("getKeywords set::find(\"foo\")",
+               result.find("foo") == result.end());
+}
+
 void
 LocaleTest::TestCreateUnicodeKeywordSet(void) {
     IcuTestErrorCode status(*this, "TestCreateUnicodeKeywordSet()");
@@ -4118,6 +4141,26 @@ LocaleTest::TestCreateUnicodeKeywordSetEmpty(void) {
     assertEquals("set::size()", 0, static_cast<int32_t>(result.size()));
 }
 
+void
+LocaleTest::TestCreateUnicodeKeywordSetWithPrivateUse(void) {
+    IcuTestErrorCode status(*this, "TestCreateUnicodeKeywordSetWithPrivateUse()");
+
+    static const char tag[] = "en-US-u-ca-gregory-x-foo";
+    static const Locale l = Locale::forLanguageTag(tag, status);
+
+    std::set<std::string> result;
+    l.getUnicodeKeywords<std::string>(
+            std::insert_iterator<decltype(result)>(result, result.begin()),
+            status);
+    status.errIfFailureAndReset("getUnicodeKeywords \"%s\"", l.getName());
+    assertTrue("getUnicodeKeywords set::find(\"ca\")",
+               result.find("ca") != result.end());
+    assertTrue("getUnicodeKeywords set::find(\"x\")",
+               result.find("x") == result.end());
+    assertTrue("getUnicodeKeywords set::find(\"foo\")",
+               result.find("foo") == result.end());
+}
+
 void
 LocaleTest::TestGetKeywordValueStdString(void) {
     IcuTestErrorCode status(*this, "TestGetKeywordValueStdString()");
diff --git a/icu4c/source/test/intltest/loctest.h b/icu4c/source/test/intltest/loctest.h
index 1fba6d94f56..05be4037bd6 100644
--- a/icu4c/source/test/intltest/loctest.h
+++ b/icu4c/source/test/intltest/loctest.h
@@ -82,8 +82,10 @@ public:
    void TestKeywordVariantParsing(void);
    void TestCreateKeywordSet(void);
    void TestCreateKeywordSetEmpty(void);
+   void TestCreateKeywordSetWithPrivateUse(void);
    void TestCreateUnicodeKeywordSet(void);
    void TestCreateUnicodeKeywordSetEmpty(void);
+   void TestCreateUnicodeKeywordSetWithPrivateUse(void);
    void TestGetKeywordValueStdString(void);
    void TestGetUnicodeKeywordValueStdString(void);
 
diff --git a/icu4j/main/tests/core/src/com/ibm/icu/dev/test/util/ULocaleTest.java b/icu4j/main/tests/core/src/com/ibm/icu/dev/test/util/ULocaleTest.java
index cbd7a4fcbb0..2e3e3b070d9 100644
--- a/icu4j/main/tests/core/src/com/ibm/icu/dev/test/util/ULocaleTest.java
+++ b/icu4j/main/tests/core/src/com/ibm/icu/dev/test/util/ULocaleTest.java
@@ -4433,6 +4433,7 @@ public class ULocaleTest extends TestFmwk {
                 //"<langtag>", "<attr1>,<attr2>,...", "<key1>,<key2>,...", "<type1>", "<type2>", ...},
                 {"en", null, null},
                 {"en-a-ext1-x-privuse", null, null},
+                {"en-a-ext1-u-ca-roc-x-privuse", null, "ca", "roc", null},
                 {"en-u-attr1-attr2", "attr1,attr2", null},
                 {"ja-u-ca-japanese-cu-jpy", null, "ca,cu", "japanese", "jpy"},
                 {"th-TH-u-number-attr-nu-thai-ca-buddhist", "attr,number", "ca,nu", "buddhist", "thai"},