diff --git a/libarchive/archive_read_support_filter_lz4.c b/libarchive/archive_read_support_filter_lz4.c
index a855f1fe..83e00ccb 100644
--- a/libarchive/archive_read_support_filter_lz4.c
+++ b/libarchive/archive_read_support_filter_lz4.c
@@ -180,6 +180,7 @@ lz4_reader_bid(struct archive_read_filter_bidder *b,
 		uint32_t frame_data_size;
 
 		/* Skip over the magic number */
+		bits_checked += 28;
 		offset_in_buffer += 4;
 
 		/* Ensure that we can read another 4 bytes. */
@@ -224,7 +225,6 @@ lz4_reader_bid(struct archive_read_filter_bidder *b,
 	 * follows, or this isn't LZ4 data.
 	 */
 
-	bits_checked = offset_in_buffer;
 	buffer = buffer + offset_in_buffer;
 
 	if (magic_number == LZ4_MAGICNUMBER) {
diff --git a/libarchive/archive_read_support_filter_zstd.c b/libarchive/archive_read_support_filter_zstd.c
index b4df94ad..c676d62b 100644
--- a/libarchive/archive_read_support_filter_zstd.c
+++ b/libarchive/archive_read_support_filter_zstd.c
@@ -105,6 +105,7 @@ zstd_bidder_bid(struct archive_read_filter_bidder *b,
 {
 	const unsigned char *buffer;
 	ssize_t avail;
+	int bits_checked = 0;
 	/*
 	 * Zstandard skippable frames contain a 4 byte magic number followed
 	 * by a 4 byte frame data size, then that number of bytes of data.
@@ -143,6 +144,7 @@ zstd_bidder_bid(struct archive_read_filter_bidder *b,
 		uint32_t frame_data_size;
 
 		/* Skip over the magic number */
+		bits_checked += 28;
 		offset_in_buffer += 4;
 
 		/* Ensure that we can read another 4 bytes. */
@@ -187,7 +189,7 @@ zstd_bidder_bid(struct archive_read_filter_bidder *b,
 	 */
 
 	if (magic_number == zstd_magic)
-		return (offset_in_buffer + 4);
+		return (bits_checked + 32);
 
 	return (0);
 }