diff --git a/builtin/cat-file.c b/builtin/cat-file.c
index 618103fdee..2dfe6265f7 100644
--- a/builtin/cat-file.c
+++ b/builtin/cat-file.c
@@ -131,7 +131,7 @@ struct expand_data {
 	unsigned char sha1[20];
 	enum object_type type;
 	unsigned long size;
-	unsigned long disk_size;
+	off_t disk_size;
 	const char *rest;
 	unsigned char delta_base_sha1[20];
 
@@ -191,7 +191,7 @@ static void expand_atom(struct strbuf *sb, const char *atom, int len,
 		if (data->mark_query)
 			data->info.disk_sizep = &data->disk_size;
 		else
-			strbuf_addf(sb, "%lu", data->disk_size);
+			strbuf_addf(sb, "%"PRIuMAX, (uintmax_t)data->disk_size);
 	} else if (is_atom("rest", atom, len)) {
 		if (data->mark_query)
 			data->split_on_whitespace = 1;
diff --git a/builtin/fsck.c b/builtin/fsck.c
index c6d17e63fd..2de272ea36 100644
--- a/builtin/fsck.c
+++ b/builtin/fsck.c
@@ -377,6 +377,10 @@ 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/builtin/index-pack.c b/builtin/index-pack.c
index e8c71fc1d2..1008d7f63c 100644
--- a/builtin/index-pack.c
+++ b/builtin/index-pack.c
@@ -338,10 +338,10 @@ static void parse_pack_header(void)
 	use(sizeof(struct pack_header));
 }
 
-static NORETURN void bad_object(unsigned long offset, const char *format,
+static NORETURN void bad_object(off_t offset, const char *format,
 		       ...) __attribute__((format (printf, 2, 3)));
 
-static NORETURN void bad_object(unsigned long offset, const char *format, ...)
+static NORETURN void bad_object(off_t offset, const char *format, ...)
 {
 	va_list params;
 	char buf[1024];
@@ -349,7 +349,8 @@ static NORETURN void bad_object(unsigned long offset, const char *format, ...)
 	va_start(params, format);
 	vsnprintf(buf, sizeof(buf), format, params);
 	va_end(params);
-	die(_("pack has bad object at offset %lu: %s"), offset, buf);
+	die(_("pack has bad object at offset %"PRIuMAX": %s"),
+	    (uintmax_t)offset, buf);
 }
 
 static inline struct thread_local *get_thread_data(void)
@@ -429,7 +430,7 @@ static int is_delta_type(enum object_type type)
 	return (type == OBJ_REF_DELTA || type == OBJ_OFS_DELTA);
 }
 
-static void *unpack_entry_data(unsigned long offset, unsigned long size,
+static void *unpack_entry_data(off_t offset, unsigned long size,
 			       enum object_type type, unsigned char *sha1)
 {
 	static char fixed_buf[8192];
@@ -549,13 +550,13 @@ static void *unpack_data(struct object_entry *obj,
 			 void *cb_data)
 {
 	off_t from = obj[0].idx.offset + obj[0].hdr_size;
-	unsigned long len = obj[1].idx.offset - from;
+	off_t len = obj[1].idx.offset - from;
 	unsigned char *data, *inbuf;
 	git_zstream stream;
 	int status;
 
 	data = xmallocz(consume ? 64*1024 : obj->size);
-	inbuf = xmalloc((len < 64*1024) ? len : 64*1024);
+	inbuf = xmalloc((len < 64*1024) ? (int)len : 64*1024);
 
 	memset(&stream, 0, sizeof(stream));
 	git_inflate_init(&stream);
@@ -563,15 +564,15 @@ static void *unpack_data(struct object_entry *obj,
 	stream.avail_out = consume ? 64*1024 : obj->size;
 
 	do {
-		ssize_t n = (len < 64*1024) ? len : 64*1024;
+		ssize_t n = (len < 64*1024) ? (ssize_t)len : 64*1024;
 		n = xpread(get_thread_data()->pack_fd, inbuf, n, from);
 		if (n < 0)
 			die_errno(_("cannot pread pack file"));
 		if (!n)
-			die(Q_("premature end of pack file, %lu byte missing",
-			       "premature end of pack file, %lu bytes missing",
-			       len),
-			    len);
+			die(Q_("premature end of pack file, %"PRIuMAX" byte missing",
+			       "premature end of pack file, %"PRIuMAX" bytes missing",
+			       (unsigned int)len),
+			    (uintmax_t)len);
 		from += n;
 		len -= n;
 		stream.next_in = inbuf;
diff --git a/builtin/pack-objects.c b/builtin/pack-objects.c
index a2f8cfdec0..92e2e5f7a8 100644
--- a/builtin/pack-objects.c
+++ b/builtin/pack-objects.c
@@ -342,15 +342,15 @@ static unsigned long write_no_reuse_object(struct sha1file *f, struct object_ent
 }
 
 /* Return 0 if we will bust the pack-size limit */
-static unsigned long write_reuse_object(struct sha1file *f, struct object_entry *entry,
-					unsigned long limit, int usable_delta)
+static off_t write_reuse_object(struct sha1file *f, struct object_entry *entry,
+				unsigned long limit, int usable_delta)
 {
 	struct packed_git *p = entry->in_pack;
 	struct pack_window *w_curs = NULL;
 	struct revindex_entry *revidx;
 	off_t offset;
 	enum object_type type = entry->type;
-	unsigned long datalen;
+	off_t datalen;
 	unsigned char header[10], dheader[10];
 	unsigned hdrlen;
 
@@ -416,11 +416,12 @@ static unsigned long write_reuse_object(struct sha1file *f, struct object_entry
 }
 
 /* Return 0 if we will bust the pack-size limit */
-static unsigned long write_object(struct sha1file *f,
-				  struct object_entry *entry,
-				  off_t write_offset)
+static off_t write_object(struct sha1file *f,
+			  struct object_entry *entry,
+			  off_t write_offset)
 {
-	unsigned long limit, len;
+	unsigned long limit;
+	off_t len;
 	int usable_delta, to_reuse;
 
 	if (!pack_to_stdout)
@@ -492,7 +493,7 @@ static enum write_one_status write_one(struct sha1file *f,
 				       struct object_entry *e,
 				       off_t *offset)
 {
-	unsigned long size;
+	off_t size;
 	int recursing;
 
 	/*
diff --git a/cache.h b/cache.h
index 3855ddfbe6..b5f76a4cf4 100644
--- a/cache.h
+++ b/cache.h
@@ -1515,7 +1515,7 @@ struct object_info {
 	/* Request */
 	enum object_type *typep;
 	unsigned long *sizep;
-	unsigned long *disk_sizep;
+	off_t *disk_sizep;
 	unsigned char *delta_base_sha1;
 	struct strbuf *typename;
 
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/sha1_file.c b/sha1_file.c
index d5e11217f5..cb571ac6e8 100644
--- a/sha1_file.c
+++ b/sha1_file.c
@@ -2281,7 +2281,7 @@ void *unpack_entry(struct packed_git *p, off_t obj_offset,
 
 		if (do_check_packed_object_crc && p->index_version > 1) {
 			struct revindex_entry *revidx = find_pack_revindex(p, obj_offset);
-			unsigned long len = revidx[1].offset - obj_offset;
+			off_t len = revidx[1].offset - obj_offset;
 			if (check_pack_crc(p, &w_curs, obj_offset, len, revidx->nr)) {
 				const unsigned char *sha1 =
 					nth_packed_object_sha1(p, revidx->nr);
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