diff --git a/icu4c/source/common/ucln_cmn.cpp b/icu4c/source/common/ucln_cmn.cpp
index 42e7019a503..2480c9d3fd2 100644
--- a/icu4c/source/common/ucln_cmn.cpp
+++ b/icu4c/source/common/ucln_cmn.cpp
@@ -14,12 +14,13 @@
 
 #include "unicode/utypes.h"
 #include "unicode/uclean.h"
-#include "utracimp.h"
-#include "ucln_cmn.h"
-#include "cmutex.h"
-#include "ucln.h"
 #include "cmemory.h"
+#include "mutex.h"
 #include "uassert.h"
+#include "ucln.h"
+#include "ucln_cmn.h"
+#include "utracimp.h"
+#include "umutex.h"
 
 /**  Auto-client for UCLN_COMMON **/
 #define UCLN_TYPE_IS_COMMON
@@ -65,6 +66,7 @@ ucln_common_registerCleanup(ECleanupCommonType type,
     U_ASSERT(UCLN_COMMON_START < type && type < UCLN_COMMON_COUNT);
     if (UCLN_COMMON_START < type && type < UCLN_COMMON_COUNT)
     {
+        icu::Mutex m;     // See ticket 10295 for discussion.
         gCommonCleanupFunctions[type] = func;
     }
 #if !UCLN_NO_AUTO_CLEANUP && (defined(UCLN_AUTO_ATEXIT) || defined(UCLN_AUTO_LOCAL))
@@ -72,6 +74,10 @@ ucln_common_registerCleanup(ECleanupCommonType type,
 #endif
 }
 
+// Note: ucln_registerCleanup() is called with the ICU global mutex locked.
+//       Be aware if adding anything to the function.
+//       See ticket 10295 for discussion.
+
 U_CAPI void U_EXPORT2
 ucln_registerCleanup(ECleanupLibraryType type,
                      cleanupFunc *func)
diff --git a/icu4c/source/i18n/ucln_in.cpp b/icu4c/source/i18n/ucln_in.cpp
index ee2a6f1dbba..431d43161e7 100644
--- a/icu4c/source/i18n/ucln_in.cpp
+++ b/icu4c/source/i18n/ucln_in.cpp
@@ -16,6 +16,7 @@
 
 #include "ucln.h"
 #include "ucln_in.h"
+#include "mutex.h"
 #include "uassert.h"
 
 /**  Auto-client for UCLN_I18N **/
@@ -46,13 +47,14 @@ static UBool i18n_cleanup(void)
 }
 
 void ucln_i18n_registerCleanup(ECleanupI18NType type,
-                               cleanupFunc *func)
-{
+                               cleanupFunc *func) {
     U_ASSERT(UCLN_I18N_START < type && type < UCLN_I18N_COUNT);
-    ucln_registerCleanup(UCLN_I18N, i18n_cleanup);
-    if (UCLN_I18N_START < type && type < UCLN_I18N_COUNT)
     {
-        gCleanupFunctions[type] = func;
+        icu::Mutex m;   // See ticket 10295 for discussion.
+        ucln_registerCleanup(UCLN_I18N, i18n_cleanup);
+        if (UCLN_I18N_START < type && type < UCLN_I18N_COUNT) {
+            gCleanupFunctions[type] = func;
+        }
     }
 #if !UCLN_NO_AUTO_CLEANUP && (defined(UCLN_AUTO_ATEXIT) || defined(UCLN_AUTO_LOCAL))
     ucln_registerAutomaticCleanup();
diff --git a/icu4c/source/io/ucln_io.cpp b/icu4c/source/io/ucln_io.cpp
index ab7b5d9c122..1775d5c5094 100644
--- a/icu4c/source/io/ucln_io.cpp
+++ b/icu4c/source/io/ucln_io.cpp
@@ -14,6 +14,7 @@
 *   created by: George Rhoten
 */
 
+#include "mutex.h"
 #include "ucln.h"
 #include "ucln_io.h"
 #include "uassert.h"
@@ -51,13 +52,14 @@ static UBool io_cleanup(void)
 }
 
 void ucln_io_registerCleanup(ECleanupIOType type,
-                               cleanupFunc *func)
-{
+                               cleanupFunc *func) {
     U_ASSERT(UCLN_IO_START < type && type < UCLN_IO_COUNT);
-    ucln_registerCleanup(UCLN_IO, io_cleanup);
-    if (UCLN_IO_START < type && type < UCLN_IO_COUNT)
     {
-        gCleanupFunctions[type] = func;
+        icu::Mutex m;       // See ticket 10295 for discussion.
+        ucln_registerCleanup(UCLN_IO, io_cleanup);
+        if (UCLN_IO_START < type && type < UCLN_IO_COUNT) {
+            gCleanupFunctions[type] = func;
+        }
     }
 
 #if !UCLN_NO_AUTO_CLEANUP && (defined(UCLN_AUTO_ATEXIT) || defined(UCLN_AUTO_LOCAL))