diff --git a/icu4c/source/test/intltest/dtfmtrtts.cpp b/icu4c/source/test/intltest/dtfmtrtts.cpp
index 21874aceb18..6d4b76da925 100644
--- a/icu4c/source/test/intltest/dtfmtrtts.cpp
+++ b/icu4c/source/test/intltest/dtfmtrtts.cpp
@@ -263,8 +263,10 @@ void DateFormatRoundTripTest::test(const Locale& loc)
     for(int32_t dstyle = DateFormat::FULL; dstyle <= DateFormat::SHORT; ++dstyle) {
         for(int32_t tstyle = DateFormat::FULL; tstyle <= DateFormat::SHORT; ++tstyle) {
             if(TEST_TABLE[itable++]) {
-                if (uprv_strcmp(loc.getLanguage(), "ccp")==0 && logKnownIssue("13366", "Skip ccp formats with zzzz,a until DateFormat parsing is fixed") &&
-                        (dstyle==DateFormat::SHORT && tstyle<= DateFormat::LONG || dstyle==DateFormat::MEDIUM && tstyle>= DateFormat::MEDIUM)) {
+                if (uprv_strcmp(loc.getLanguage(),"ccp")==0 && logKnownIssue("13366", "Skip handling ccp until DateFormat parsing is fixed")) {
+                    continue;
+                }
+                if (uprv_strcmp(loc.getLanguage(),"fa")==0 && tstyle==DateFormat::FULL && logKnownIssue("13374", "Skip handling fa until TimeZone roundtrip is fixed")) {
                     continue;
                 }
                 logln("Testing dstyle" + UnicodeString(styleName((DateFormat::EStyle)dstyle)) + ", tstyle" + UnicodeString(styleName((DateFormat::EStyle)tstyle)) );
diff --git a/icu4c/source/test/intltest/nmfmtrt.cpp b/icu4c/source/test/intltest/nmfmtrt.cpp
index 33b4c0927a5..54226a54710 100644
--- a/icu4c/source/test/intltest/nmfmtrt.cpp
+++ b/icu4c/source/test/intltest/nmfmtrt.cpp
@@ -16,6 +16,7 @@
 #include "unicode/decimfmt.h"
 #include "unicode/locid.h"
 #include "putilimp.h"
+#include "cstring.h"
 
 #include <float.h>
 #include <stdio.h>    // for sprintf
@@ -122,6 +123,9 @@ NumberFormatRoundTripTest::start()
         logln("Quick mode: only testing first 5 Locales");
     }
     for(int i = 0; i < locCount; ++i) {
+        if (uprv_strcmp(loc[i].getLanguage(),"ccp")==0 && logKnownIssue("13366", "Skip handling ccp until NumberFormat parsing is fixed")) {
+            continue;
+        }
         UnicodeString name;
         logln(loc[i].getDisplayName(name));
 
@@ -343,10 +347,13 @@ NumberFormatRoundTripTest::escape(UnicodeString& s)
     UnicodeString copy(s);
     s.remove();
     for(int i = 0; i < copy.length(); ++i) {
-        UChar c = copy[i];
-        if(c < 0x00FF) 
+        UChar32 c = copy.char32At(i);
+        if (c >= 0x10000) {
+            ++i;
+        }
+        if(c < 0x00FF) {
             s += c;
-        else {
+        } else {
             s += "+U";
             char temp[16];
             sprintf(temp, "%4X", c);        // might not work
diff --git a/icu4c/source/test/intltest/tsdate.cpp b/icu4c/source/test/intltest/tsdate.cpp
index 15d8a570b74..68806b8c2e5 100644
--- a/icu4c/source/test/intltest/tsdate.cpp
+++ b/icu4c/source/test/intltest/tsdate.cpp
@@ -13,6 +13,7 @@
 #include "unicode/smpdtfmt.h"
 #include "tsdate.h"
 #include "putilimp.h"
+#include "cstring.h"
 
 #include <float.h>
 #include <stdlib.h>
@@ -280,6 +281,9 @@ void IntlTestDateFormat::monsterTest(/*char *par*/)
         }
         for (int32_t i=0; i<count; ++i)
         {
+            if (uprv_strcmp(locales[i].getLanguage(),"ccp")==0 && logKnownIssue("13366", "Skip handling ccp until DateFormat parsing is fixed")) {
+                continue;
+            }
             UnicodeString name = UnicodeString(locales[i].getName(), "");
             logln((UnicodeString)"Testing " + name + "...");
             testLocale(/*par, */locales[i], name);
diff --git a/icu4c/source/test/intltest/tsnmfmt.cpp b/icu4c/source/test/intltest/tsnmfmt.cpp
index 845206f266e..e326f556cba 100644
--- a/icu4c/source/test/intltest/tsnmfmt.cpp
+++ b/icu4c/source/test/intltest/tsnmfmt.cpp
@@ -442,6 +442,9 @@ void IntlTestNumberFormat::monsterTest(/* char* par */)
         }
         for (int32_t i=0; i<count; ++i)
         {
+            if (uprv_strcmp(locales[i].getLanguage(),"ccp")==0 && logKnownIssue("13366", "Skip handling ccp until NumberFormat parsing is fixed")) {
+                continue;
+            }
             UnicodeString name(locales[i].getName(), "");
             logln(SEP);
             testLocale(/* par, */locales[i], name);
diff --git a/icu4c/source/test/intltest/tzfmttst.cpp b/icu4c/source/test/intltest/tzfmttst.cpp
index b74ee5ffc71..d2a841f5433 100644
--- a/icu4c/source/test/intltest/tzfmttst.cpp
+++ b/icu4c/source/test/intltest/tzfmttst.cpp
@@ -159,6 +159,12 @@ TimeZoneFormatTest::TestTimeZoneRoundTrip(void) {
 
     // Run the roundtrip test
     for (int32_t locidx = 0; locidx < nLocales; locidx++) {
+        if (uprv_strcmp(LOCALES[locidx].getLanguage(),"ccp")==0 && logKnownIssue("13366", "Skip handling ccp until TimeZone offset roundtrip is fixed")) {
+            continue;
+        }
+        if (uprv_strcmp(LOCALES[locidx].getLanguage(),"fa")==0 && logKnownIssue("13374", "Skip handling fa until TimeZone offset roundtrip is fixed")) {
+            continue;
+        }
         UnicodeString localGMTString;
         SimpleDateFormat gmtFmt(UnicodeString("ZZZZ"), LOCALES[locidx], status);
         if (U_FAILURE(status)) {