diff --git a/builtin/fsck.c b/builtin/fsck.c
index 55eac756f7..b08bc8be24 100644
--- a/builtin/fsck.c
+++ b/builtin/fsck.c
@@ -356,6 +356,10 @@ static int fsck_sha1(const unsigned char *sha1)
 static int fsck_obj_buffer(const unsigned char *sha1, enum object_type type,
 			   unsigned long size, void *buffer, int *eaten)
 {
+	/*
+	 * Note, buffer may be NULL if type is OBJ_BLOB. See
+	 * verify_packfile(), data_valid variable for details.
+	 */
 	struct object *obj;
 	obj = parse_object_buffer(sha1, type, size, buffer, eaten);
 	if (!obj) {
diff --git a/pack-check.c b/pack-check.c
index 1da89a41ce..d123846ea2 100644
--- a/pack-check.c
+++ b/pack-check.c
@@ -105,6 +105,8 @@ static int verify_packfile(struct packed_git *p,
 		void *data;
 		enum object_type type;
 		unsigned long size;
+		off_t curpos;
+		int data_valid;
 
 		if (p->index_version > 1) {
 			off_t offset = entries[i].offset;
@@ -116,8 +118,25 @@ static int verify_packfile(struct packed_git *p,
 					    sha1_to_hex(entries[i].sha1),
 					    p->pack_name, (uintmax_t)offset);
 		}
-		data = unpack_entry(p, entries[i].offset, &type, &size);
-		if (!data)
+
+		curpos = entries[i].offset;
+		type = unpack_object_header(p, w_curs, &curpos, &size);
+		unuse_pack(w_curs);
+
+		if (type == OBJ_BLOB && big_file_threshold <= size) {
+			/*
+			 * Let check_sha1_signature() check it with
+			 * the streaming interface; no point slurping
+			 * the data in-core only to discard.
+			 */
+			data = NULL;
+			data_valid = 0;
+		} else {
+			data = unpack_entry(p, entries[i].offset, &type, &size);
+			data_valid = 1;
+		}
+
+		if (data_valid && !data)
 			err = error("cannot unpack %s from %s at offset %"PRIuMAX"",
 				    sha1_to_hex(entries[i].sha1), p->pack_name,
 				    (uintmax_t)entries[i].offset);
diff --git a/pack.h b/pack.h
index 3223f5a038..0e77429df5 100644
--- a/pack.h
+++ b/pack.h
@@ -74,6 +74,7 @@ struct pack_idx_entry {
 
 
 struct progress;
+/* Note, the data argument could be NULL if object type is blob */
 typedef int (*verify_fn)(const unsigned char*, enum object_type, unsigned long, void*, int*);
 
 extern const char *write_idx_file(const char *index_name, struct pack_idx_entry **objects, int nr_objects, const struct pack_idx_option *, const unsigned char *sha1);
diff --git a/t/t1050-large.sh b/t/t1050-large.sh
index f9f3d1391f..096dbffecc 100755
--- a/t/t1050-large.sh
+++ b/t/t1050-large.sh
@@ -177,10 +177,9 @@ test_expect_success 'zip achiving, deflate' '
 	git archive --format=zip HEAD >/dev/null
 '
 
-test_expect_success 'fsck' '
-	test_must_fail git fsck 2>err &&
-	n=$(grep "error: attempting to allocate .* over limit" err | wc -l) &&
-	test "$n" -gt 1
+test_expect_success 'fsck large blobs' '
+	git fsck 2>err &&
+	test_must_be_empty err
 '
 
 test_done