diff --git a/memcheck/mac_replace_strmem.c b/memcheck/mac_replace_strmem.c
index 4e4ec3d7a..1a9255eb4 100644
--- a/memcheck/mac_replace_strmem.c
+++ b/memcheck/mac_replace_strmem.c
@@ -186,13 +186,15 @@ char* strcpy ( char* dst, const char* src )
 
 char* strncpy ( char* dst, const char* src, int n )
 {
-   Char* dst_orig = dst;
+   const Char* src_orig = src;
+         Char* dst_orig = dst;
    Int   m = 0;
 
-   if (is_overlap(dst, src, n, n))
-      complain3("strncpy", dst, src, n);
-
    while (m   < n && *src) { m++; *dst++ = *src++; }
+   /* Check for overlap after copying; all n bytes of dst are relevant,
+      but only m+1 bytes of src if terminator was found */
+   if (is_overlap(dst_orig, src_orig, n, (m < n) ? m+1 : n))
+      complain3("strncpy", dst, src, n);
    while (m++ < n) *dst++ = 0;         /* must pad remainder with nulls */
 
    return dst_orig;
diff --git a/memcheck/tests/overlap.c b/memcheck/tests/overlap.c
index 60e14c20f..d868886f3 100644
--- a/memcheck/tests/overlap.c
+++ b/memcheck/tests/overlap.c
@@ -112,5 +112,14 @@ int main(void)
       strncat(a+20, a, 21);    // run twice to check 2nd error isn't shown
    strncat(a, a+20, 21);
 
+   /* This is ok, but once gave a warning when strncpy() was wrong,
+      and used 'n' for the length, even when the src was shorter than 'n' */
+   {
+      char dest[64];
+      char src [16];
+      strcpy( src, "short" );
+      strncpy( dest, src, 20 );
+   }
+
    return 0;
 }