diff --git a/icu4c/source/common/cmemory.h b/icu4c/source/common/cmemory.h
index f997d9224f8..3041b56d1a1 100644
--- a/icu4c/source/common/cmemory.h
+++ b/icu4c/source/common/cmemory.h
@@ -207,6 +207,14 @@ public:
         LocalPointerBase<T>::ptr=other.ptr;
         other.ptr=temp;
     }
+    /**
+     * Non-member LocalMemory swap function.
+     * @param p1 will get p2's pointer
+     * @param p2 will get p1's pointer
+     */
+    friend inline void swap(LocalMemory<T> &p1, LocalMemory<T> &p2) U_NOEXCEPT {
+        p1.swap(p2);
+    }
     /**
      * Deletes the array it owns,
      * and adopts (takes ownership of) the one passed in.
@@ -246,16 +254,6 @@ public:
     T &operator[](ptrdiff_t i) const { return LocalPointerBase<T>::ptr[i]; }
 };
 
-/**
- * Non-member LocalMemory swap function.
- * @param p1 will get p2's pointer
- * @param p2 will get p1's pointer
- */
-template<typename T>
-inline void swap(LocalMemory<T> &p1, LocalMemory<T> &p2) U_NOEXCEPT {
-    p1.swap(p2);
-}
-
 template<typename T>
 inline T *LocalMemory<T>::allocateInsteadAndReset(int32_t newCapacity) {
     if(newCapacity>0) {
diff --git a/icu4c/source/common/unicode/localpointer.h b/icu4c/source/common/unicode/localpointer.h
index a46a0d25d5f..fff986b67fa 100644
--- a/icu4c/source/common/unicode/localpointer.h
+++ b/icu4c/source/common/unicode/localpointer.h
@@ -266,6 +266,15 @@ public:
         LocalPointerBase<T>::ptr=other.ptr;
         other.ptr=temp;
     }
+    /**
+     * Non-member LocalPointer swap function.
+     * @param p1 will get p2's pointer
+     * @param p2 will get p1's pointer
+     * @draft ICU 56
+     */
+    friend inline void swap(LocalPointer<T> &p1, LocalPointer<T> &p2) U_NOEXCEPT {
+        p1.swap(p2);
+    }
 #endif  /* U_HIDE_DRAFT_API */
     /**
      * Deletes the object it owns,
@@ -307,19 +316,6 @@ public:
 #endif  /* U_HIDE_DRAFT_API */
 };
 
-#ifndef U_HIDE_DRAFT_API
-/**
- * Non-member LocalPointer swap function.
- * @param p1 will get p2's pointer
- * @param p2 will get p1's pointer
- * @draft ICU 56
- */
-template<typename T>
-inline void swap(LocalPointer<T> &p1, LocalPointer<T> &p2) U_NOEXCEPT {
-    p1.swap(p2);
-}
-#endif  /* U_HIDE_DRAFT_API */
-
 /**
  * "Smart pointer" class, deletes objects via the C++ array delete[] operator.
  * For most methods see the LocalPointerBase base class.
@@ -422,6 +418,15 @@ public:
         LocalPointerBase<T>::ptr=other.ptr;
         other.ptr=temp;
     }
+    /**
+     * Non-member LocalArray swap function.
+     * @param p1 will get p2's pointer
+     * @param p2 will get p1's pointer
+     * @draft ICU 56
+     */
+    friend inline void swap(LocalArray<T> &p1, LocalArray<T> &p2) U_NOEXCEPT {
+        p1.swap(p2);
+    }
 #endif  /* U_HIDE_DRAFT_API */
     /**
      * Deletes the array it owns,
@@ -471,19 +476,6 @@ public:
     T &operator[](ptrdiff_t i) const { return LocalPointerBase<T>::ptr[i]; }
 };
 
-#ifndef U_HIDE_DRAFT_API
-/**
- * Non-member LocalArray swap function.
- * @param p1 will get p2's pointer
- * @param p2 will get p1's pointer
- * @draft ICU 56
- */
-template<typename T>
-inline void swap(LocalArray<T> &p1, LocalArray<T> &p2) U_NOEXCEPT {
-    p1.swap(p2);
-}
-#endif  /* U_HIDE_DRAFT_API */
-
 /**
  * \def U_DEFINE_LOCAL_OPEN_POINTER
  * "Smart pointer" definition macro, deletes objects via the closeFunction.
@@ -531,15 +523,14 @@ inline void swap(LocalArray<T> &p1, LocalArray<T> &p2) U_NOEXCEPT {
             LocalPointerBase<Type>::ptr=other.ptr; \
             other.ptr=temp; \
         } \
+        friend inline void swap(LocalPointerClassName &p1, LocalPointerClassName &p2) U_NOEXCEPT { \
+            p1.swap(p2); \
+        } \
         void adoptInstead(Type *p) { \
             closeFunction(ptr); \
             ptr=p; \
         } \
-    }; \
-    inline void swap(LocalPointerClassName &p1, LocalPointerClassName &p2) U_NOEXCEPT { \
-        p1.swap(p2); \
-    } \
-    class LocalPointerClassName
+    }
 #else
 #define U_DEFINE_LOCAL_OPEN_POINTER(LocalPointerClassName, Type, closeFunction) \
     class LocalPointerClassName : public LocalPointerBase<Type> { \
@@ -557,19 +548,15 @@ inline void swap(LocalArray<T> &p1, LocalArray<T> &p2) U_NOEXCEPT {
             LocalPointerBase<Type>::ptr=other.ptr; \
             other.ptr=temp; \
         } \
+        friend inline void swap(LocalPointerClassName &p1, LocalPointerClassName &p2) U_NOEXCEPT { \
+            p1.swap(p2); \
+        } \
         void adoptInstead(Type *p) { \
             closeFunction(ptr); \
             ptr=p; \
         } \
-    }; \
-    inline void swap(LocalPointerClassName &p1, LocalPointerClassName &p2) U_NOEXCEPT { \
-        p1.swap(p2); \
-    } \
-    class LocalPointerClassName
+    }
 #endif
-// The trailing class forward declaration at the end of U_DEFINE_LOCAL_OPEN_POINTER
-// prevents a warning or error from -pedantic compilation
-// due to an extra ';' after the non-member swap function definition.
 
 U_NAMESPACE_END
 
diff --git a/icu4c/source/common/unicode/unistr.h b/icu4c/source/common/unicode/unistr.h
index 179b9c2666b..dfcc8def2fc 100644
--- a/icu4c/source/common/unicode/unistr.h
+++ b/icu4c/source/common/unicode/unistr.h
@@ -1909,6 +1909,17 @@ public:
    * @draft ICU 56
    */
   void swap(UnicodeString &other) U_NOEXCEPT;
+
+  /**
+   * Non-member UnicodeString swap function.
+   * @param s1 will get s2's contents and state
+   * @param s2 will get s1's contents and state
+   * @draft ICU 56
+   */
+  friend U_COMMON_API inline void U_EXPORT2
+  swap(UnicodeString &s1, UnicodeString &s2) U_NOEXCEPT {
+    s1.swap(s2);
+  }
 #endif  /* U_HIDE_DRAFT_API */
 
   /**
@@ -3668,19 +3679,6 @@ private:
 U_COMMON_API UnicodeString U_EXPORT2
 operator+ (const UnicodeString &s1, const UnicodeString &s2);
 
-#ifndef U_HIDE_DRAFT_API
-/**
- * Non-member UnicodeString swap function.
- * @param s1 will get s2's contents and state
- * @param s2 will get s1's contents and state
- * @draft ICU 56
- */
-U_COMMON_API inline void U_EXPORT2
-swap(UnicodeString &s1, UnicodeString &s2) U_NOEXCEPT {
-    s1.swap(s2);
-}
-#endif  /* U_HIDE_DRAFT_API */
-
 //========================================
 // Inline members
 //========================================
diff --git a/icu4c/source/common/unistr.cpp b/icu4c/source/common/unistr.cpp
index bd53c5a77c5..4b4a53eafba 100644
--- a/icu4c/source/common/unistr.cpp
+++ b/icu4c/source/common/unistr.cpp
@@ -556,8 +556,12 @@ void UnicodeString::copyFieldsFrom(UnicodeString &src, UBool setSrcToBogus) U_NO
   int16_t lengthAndFlags = fUnion.fFields.fLengthAndFlags = src.fUnion.fFields.fLengthAndFlags;
   if(lengthAndFlags & kUsingStackBuffer) {
     // Short string using the stack buffer, copy the contents.
-    uprv_memcpy(fUnion.fStackFields.fBuffer, src.fUnion.fStackFields.fBuffer,
-                getShortLength() * U_SIZEOF_UCHAR);
+    // Check for self assignment to prevent "overlap in memcpy" warnings,
+    // although it should be harmless to copy a buffer to itself exactly.
+    if(this != &src) {
+      uprv_memcpy(fUnion.fStackFields.fBuffer, src.fUnion.fStackFields.fBuffer,
+                  getShortLength() * U_SIZEOF_UCHAR);
+    }
   } else {
     // In all other cases, copy all fields.
     fUnion.fFields.fArray = src.fUnion.fFields.fArray;