diff --git a/icu4c/source/test/cintltst/ccapitst.c b/icu4c/source/test/cintltst/ccapitst.c
index c16a0636d4b..85eba913a10 100644
--- a/icu4c/source/test/cintltst/ccapitst.c
+++ b/icu4c/source/test/cintltst/ccapitst.c
@@ -190,10 +190,22 @@ static void TestConvert()
     else {
         const char *string = NULL;
         int32_t len = 0;
+        int32_t count1 = 0;
+        int32_t count2 = 0;
         allNamesCount = uenum_count(allNamesEnum, &err);
         while ((string = uenum_next(allNamesEnum, &len, &err))) {
+            count1++;
             log_verbose("read \"%s\", length %i\n", string, len);
         }
+        err = U_ZERO_ERROR;
+        uenum_reset(allNamesEnum, &err);
+        while ((string = uenum_next(allNamesEnum, &len, &err))) {
+            count2++;
+            log_verbose("read \"%s\", length %i\n", string, len);
+        }
+        if (count1 != count2) {
+            log_err("FAILURE! uenum_reset(allNamesEnum, &err); doesn't work\n");
+        }
     }
     uenum_close(allNamesEnum);
     err = U_ZERO_ERROR;
diff --git a/icu4c/source/test/cintltst/stdnmtst.c b/icu4c/source/test/cintltst/stdnmtst.c
index 919ab65376e..a8d85a1e6b3 100644
--- a/icu4c/source/test/cintltst/stdnmtst.c
+++ b/icu4c/source/test/cintltst/stdnmtst.c
@@ -147,6 +147,8 @@ static void TestCanonicalName()
         dotestconv("cp1208", "", "UTF-8") &&        /* default name due to ordering */
         dotestconv("cp65001", "", "UTF-8") &&        /* non-default name due to ordering */
         dotestconv("ISO-2022", "MIME", "ISO_2022") &&/* default name */
+        dotestconv("Shift_JIS", "MIME", "ibm-943_P14A-2000") &&/* ambiguous alias */
+        dotestconv("Shift_JIS", "", "ibm-943_P130-2000") &&/* ambiguous alias */
         dotestconv("crazy", "MIME", NULL) &&
         dotestconv("ASCII", "crazy", NULL))
     {