diff --git a/icu4c/source/i18n/alphaindex.cpp b/icu4c/source/i18n/alphaindex.cpp
index 1b02e050880..e94cdccdd2b 100644
--- a/icu4c/source/i18n/alphaindex.cpp
+++ b/icu4c/source/i18n/alphaindex.cpp
@@ -117,6 +117,11 @@ int32_t binarySearch(const UVector &list, const UnicodeString &s, const Collator
     }
 }
 
+}  // namespace
+
+// The BucketList is not in the anonymous namespace because only Clang
+// seems to support its use in other classes from there.
+// However, we also don't need U_I18N_API because it is not used from outside the i18n library.
 class BucketList : public UObject {
 public:
     BucketList(UVector *bucketList, UVector *publicBucketList)
@@ -167,8 +172,6 @@ public:
     UVector *immutableVisibleList_;
 };
 
-}  // namespace
-
 AlphabeticIndex::ImmutableIndex::~ImmutableIndex() {
     delete buckets_;
     delete collatorPrimaryOnly_;
diff --git a/icu4c/source/i18n/unicode/alphaindex.h b/icu4c/source/i18n/unicode/alphaindex.h
index 1fb234e8982..64e2f5434ba 100644
--- a/icu4c/source/i18n/unicode/alphaindex.h
+++ b/icu4c/source/i18n/unicode/alphaindex.h
@@ -71,12 +71,7 @@ U_NAMESPACE_BEGIN
 
 // Forward Declarations
 
-namespace {
-
 class BucketList;
-
-}  // namespace;
-
 class Collator;
 class RuleBasedCollator;
 class StringEnumeration;
diff --git a/icu4c/source/test/intltest/alphaindextst.cpp b/icu4c/source/test/intltest/alphaindextst.cpp
index 8e70dcfa18c..9e7e75f123a 100644
--- a/icu4c/source/test/intltest/alphaindextst.cpp
+++ b/icu4c/source/test/intltest/alphaindextst.cpp
@@ -7,6 +7,8 @@
 //   file:  alphaindex.cpp
 //          Alphabetic Index Tests.
 //
+#include <stdio.h>  // for sprintf
+
 #include "intltest.h"
 #include "alphaindextst.h"