diff --git a/src/include/common/hashfn_unstable.h b/src/include/common/hashfn_unstable.h
index 0263b653dd..7b647470ab 100644
--- a/src/include/common/hashfn_unstable.h
+++ b/src/include/common/hashfn_unstable.h
@@ -219,6 +219,13 @@ fasthash_accum(fasthash_state *hs, const char *k, size_t len)
 #define haszero64(v) \
 	(((v) - 0x0101010101010101) & ~(v) & 0x8080808080808080)
 
+/* get first byte in memory order */
+#ifdef WORDS_BIGENDIAN
+#define firstbyte64(v) ((v) >> 56)
+#else
+#define firstbyte64(v) ((v) & 0xFF)
+#endif
+
 /*
  * all-purpose workhorse for fasthash_accum_cstring
  */
@@ -255,7 +262,7 @@ static inline size_t
 fasthash_accum_cstring_aligned(fasthash_state *hs, const char *str)
 {
 	const char *const start = str;
-	size_t		remainder;
+	uint64		chunk;
 	uint64		zero_byte_low;
 
 	Assert(PointerIsAligned(start, uint64));
@@ -275,7 +282,7 @@ fasthash_accum_cstring_aligned(fasthash_state *hs, const char *str)
 	 */
 	for (;;)
 	{
-		uint64		chunk = *(uint64 *) str;
+		chunk = *(uint64 *) str;
 
 #ifdef WORDS_BIGENDIAN
 		zero_byte_low = haszero64(pg_bswap64(chunk));
@@ -290,14 +297,33 @@ fasthash_accum_cstring_aligned(fasthash_state *hs, const char *str)
 		str += FH_SIZEOF_ACCUM;
 	}
 
-	/*
-	 * The byte corresponding to the NUL will be 0x80, so the rightmost bit
-	 * position will be in the range 7, 15, ..., 63. Turn this into byte
-	 * position by dividing by 8.
-	 */
-	remainder = pg_rightmost_one_pos64(zero_byte_low) / BITS_PER_BYTE;
-	fasthash_accum(hs, str, remainder);
-	str += remainder;
+	if (firstbyte64(chunk) != 0)
+	{
+		size_t		remainder;
+		uint64		mask;
+
+		/*
+		 * The byte corresponding to the NUL will be 0x80, so the rightmost
+		 * bit position will be in the range 15, 23, ..., 63. Turn this into
+		 * byte position by dividing by 8.
+		 */
+		remainder = pg_rightmost_one_pos64(zero_byte_low) / BITS_PER_BYTE;
+
+		/*
+		 * Create a mask for the remaining bytes so we can combine them into
+		 * the hash. This must have the same result as mixing the remaining
+		 * bytes with fasthash_accum().
+		 */
+#ifdef WORDS_BIGENDIAN
+		mask = ~UINT64CONST(0) << BITS_PER_BYTE * (FH_SIZEOF_ACCUM - remainder);
+#else
+		mask = ~UINT64CONST(0) >> BITS_PER_BYTE * (FH_SIZEOF_ACCUM - remainder);
+#endif
+		hs->accum = chunk & mask;
+		fasthash_combine(hs);
+
+		str += remainder;
+	}
 
 	return str - start;
 }