diff --git a/coregrind/stage1.c b/coregrind/stage1.c
index ce408d7..4fab733 100644
--- a/coregrind/stage1.c
+++ b/coregrind/stage1.c
@@ -149,7 +149,7 @@
    /* If we didn't see all the entries we need to fix up, then we
       can't make the new executable viable. */
    if (seen != 0xf) {
-      fprintf(stderr, "fix_auxv: we didn't see enough auxv entries (seen=%x)\n", seen);
+      fprintf(stderr, "valgrind: we didn't see enough auxv entries (seen=%x)\n", seen);
       exit(1);
    }
 
@@ -188,7 +188,7 @@
    err = do_exec(buf, &info);
 
    if (err != 0) {
-      fprintf(stderr, "failed to load %s: %s\n",
+      fprintf(stderr, "valgrind: failed to load %s: %s\n",
 	      buf, strerror(err));
       exit(1);
    }
diff --git a/coregrind/ume.c b/coregrind/ume.c
index d7c1880..735904d 100644
--- a/coregrind/ume.c
+++ b/coregrind/ume.c
@@ -491,7 +491,9 @@
       if (minaddr >= maxaddr ||
 	  (minaddr < info->exe_base ||
 	   maxaddr > info->exe_end)) {
-	 fprintf(stderr, "Executable is mapped outside of range %p-%p\n",
+	 fprintf(stderr, "Executable range %p-%p is outside the\n"
+                         "acceptable range %p-%p\n",
+		 (void *)minaddr,        (void *)maxaddr,
 		 (void *)info->exe_base, (void *)info->exe_end);
 	 return ENOMEM;
       }