diff --git a/builtin/pack-objects.c b/builtin/pack-objects.c
index 0d80dee2ba..1bd43432f7 100644
--- a/builtin/pack-objects.c
+++ b/builtin/pack-objects.c
@@ -40,6 +40,7 @@
 #define DELTA_CHILD(obj) oe_delta_child(&to_pack, obj)
 #define DELTA_SIBLING(obj) oe_delta_sibling(&to_pack, obj)
 #define SET_DELTA(obj, val) oe_set_delta(&to_pack, obj, val)
+#define SET_DELTA_EXT(obj, oid) oe_set_delta_ext(&to_pack, obj, oid)
 #define SET_DELTA_SIZE(obj, val) oe_set_delta_size(&to_pack, obj, val)
 #define SET_DELTA_CHILD(obj, val) oe_set_delta_child(&to_pack, obj, val)
 #define SET_DELTA_SIBLING(obj, val) oe_set_delta_sibling(&to_pack, obj, val)
@@ -59,6 +60,7 @@ static struct packing_data to_pack;
 
 static struct pack_idx_entry **written_list;
 static uint32_t nr_result, nr_written, nr_seen;
+static struct bitmap_index *bitmap_git;
 
 static int non_empty;
 static int reuse_delta = 1, reuse_object = 1;
@@ -79,6 +81,7 @@ static unsigned long pack_size_limit;
 static int depth = 50;
 static int delta_search_threads;
 static int pack_to_stdout;
+static int thin;
 static int num_preferred_base;
 static struct progress *progress_state;
 
@@ -1510,11 +1513,15 @@ static void check_object(struct object_entry *entry)
 			break;
 		}
 
-		if (base_ref && (base_entry = packlist_find(&to_pack, base_ref, NULL))) {
+		if (base_ref && (
+		    (base_entry = packlist_find(&to_pack, base_ref, NULL)) ||
+		    (thin &&
+		     bitmap_has_sha1_in_uninteresting(bitmap_git, base_ref)))) {
 			/*
 			 * If base_ref was set above that means we wish to
-			 * reuse delta data, and we even found that base
-			 * in the list of objects we want to pack. Goodie!
+			 * reuse delta data, and either we found that object in
+			 * the list of objects we want to pack, or it's one we
+			 * know the receiver has.
 			 *
 			 * Depth value does not matter - find_deltas() will
 			 * never consider reused delta as the base object to
@@ -1523,10 +1530,16 @@ static void check_object(struct object_entry *entry)
 			 */
 			oe_set_type(entry, entry->in_pack_type);
 			SET_SIZE(entry, in_pack_size); /* delta size */
-			SET_DELTA(entry, base_entry);
 			SET_DELTA_SIZE(entry, in_pack_size);
-			entry->delta_sibling_idx = base_entry->delta_child_idx;
-			SET_DELTA_CHILD(base_entry, entry);
+
+			if (base_entry) {
+				SET_DELTA(entry, base_entry);
+				entry->delta_sibling_idx = base_entry->delta_child_idx;
+				SET_DELTA_CHILD(base_entry, entry);
+			} else {
+				SET_DELTA_EXT(entry, base_ref);
+			}
+
 			unuse_pack(&w_curs);
 			return;
 		}
@@ -2954,7 +2967,6 @@ static int pack_options_allow_reuse(void)
 
 static int get_object_list_from_bitmap(struct rev_info *revs)
 {
-	struct bitmap_index *bitmap_git;
 	if (!(bitmap_git = prepare_bitmap_walk(revs)))
 		return -1;
 
@@ -2970,7 +2982,6 @@ static int get_object_list_from_bitmap(struct rev_info *revs)
 	}
 
 	traverse_bitmap_commit_list(bitmap_git, &add_object_entry_from_bitmap);
-	free_bitmap_index(bitmap_git);
 	return 0;
 }
 
@@ -3118,7 +3129,6 @@ static int option_parse_unpack_unreachable(const struct option *opt,
 int cmd_pack_objects(int argc, const char **argv, const char *prefix)
 {
 	int use_internal_rev_list = 0;
-	int thin = 0;
 	int shallow = 0;
 	int all_progress_implied = 0;
 	struct argv_array rp = ARGV_ARRAY_INIT;
diff --git a/pack-objects.c b/pack-objects.c
index 92708522e7..9ae0cecd81 100644
--- a/pack-objects.c
+++ b/pack-objects.c
@@ -177,3 +177,22 @@ struct object_entry *packlist_alloc(struct packing_data *pdata,
 
 	return new_entry;
 }
+
+void oe_set_delta_ext(struct packing_data *pdata,
+		      struct object_entry *delta,
+		      const unsigned char *sha1)
+{
+	struct object_entry *base;
+
+	ALLOC_GROW(pdata->ext_bases, pdata->nr_ext + 1, pdata->alloc_ext);
+	base = &pdata->ext_bases[pdata->nr_ext++];
+	memset(base, 0, sizeof(*base));
+	hashcpy(base->idx.oid.hash, sha1);
+
+	/* These flags mark that we are not part of the actual pack output. */
+	base->preferred_base = 1;
+	base->filled = 1;
+
+	delta->ext_base = 1;
+	delta->delta_idx = base - pdata->ext_bases + 1;
+}
diff --git a/pack-objects.h b/pack-objects.h
index 08c6b57d49..3fd10b15c9 100644
--- a/pack-objects.h
+++ b/pack-objects.h
@@ -111,6 +111,7 @@ struct object_entry {
 	unsigned dfs_state:OE_DFS_STATE_BITS;
 	unsigned char in_pack_header_size;
 	unsigned depth:OE_DEPTH_BITS;
+	unsigned ext_base:1; /* delta_idx points outside packlist */
 
 	/*
 	 * pahole results on 64-bit linux (gcc and clang)
@@ -141,6 +142,14 @@ struct packing_data {
 	struct packed_git **in_pack_by_idx;
 	struct packed_git **in_pack;
 
+	/*
+	 * This list contains entries for bases which we know the other side
+	 * has (e.g., via reachability bitmaps), but which aren't in our
+	 * "objects" list.
+	 */
+	struct object_entry *ext_bases;
+	uint32_t nr_ext, alloc_ext;
+
 	uintmax_t oe_size_limit;
 };
 
@@ -228,9 +237,12 @@ static inline struct object_entry *oe_delta(
 		const struct packing_data *pack,
 		const struct object_entry *e)
 {
-	if (e->delta_idx)
+	if (!e->delta_idx)
+		return NULL;
+	if (e->ext_base)
+		return &pack->ext_bases[e->delta_idx - 1];
+	else
 		return &pack->objects[e->delta_idx - 1];
-	return NULL;
 }
 
 static inline void oe_set_delta(struct packing_data *pack,
@@ -243,6 +255,10 @@ static inline void oe_set_delta(struct packing_data *pack,
 		e->delta_idx = 0;
 }
 
+void oe_set_delta_ext(struct packing_data *pack,
+		      struct object_entry *e,
+		      const unsigned char *sha1);
+
 static inline struct object_entry *oe_delta_child(
 		const struct packing_data *pack,
 		const struct object_entry *e)