diff --git a/src/basic/memory-util.c b/src/basic/memory-util.c
index 3338e355f7b..29837621176 100644
--- a/src/basic/memory-util.c
+++ b/src/basic/memory-util.c
@@ -18,26 +18,25 @@ size_t page_size(void) {
         return pgsz;
 }
 
-bool memeqzero(const void *data, size_t length) {
-        /* Does the buffer consist entirely of NULs?
+bool memeqbyte(uint8_t byte, const void *data, size_t length) {
+        /* Does the buffer consist entirely of the same specific byte value?
          * Copied from https://github.com/systemd/casync/, copied in turn from
          * https://github.com/rustyrussell/ccan/blob/master/ccan/mem/mem.c#L92,
          * which is licensed CC-0.
          */
 
         const uint8_t *p = data;
-        size_t i;
 
         /* Check first 16 bytes manually */
-        for (i = 0; i < 16; i++, length--) {
+        for (size_t i = 0; i < 16; i++, length--) {
                 if (length == 0)
                         return true;
-                if (p[i])
+                if (p[i] != byte)
                         return false;
         }
 
-        /* Now we know first 16 bytes are NUL, memcmp with self.  */
-        return memcmp(data, p + i, length) == 0;
+        /* Now we know first 16 bytes match, memcmp() with self.  */
+        return memcmp(data, p + 16, length) == 0;
 }
 
 #if !HAVE_EXPLICIT_BZERO
diff --git a/src/basic/memory-util.h b/src/basic/memory-util.h
index e2b543cb8f2..9f37431fc19 100644
--- a/src/basic/memory-util.h
+++ b/src/basic/memory-util.h
@@ -47,7 +47,9 @@ static inline int memcmp_nn(const void *s1, size_t n1, const void *s2, size_t n2
 
 #define zero(x) (memzero(&(x), sizeof(x)))
 
-bool memeqzero(const void *data, size_t length);
+bool memeqbyte(uint8_t byte, const void *data, size_t length);
+
+#define memeqzero(data, length) memeqbyte(0x00, data, length)
 
 #define eqzero(x) memeqzero(x, sizeof(x))