diff --git a/Documentation/technical/commit-graph.txt b/Documentation/technical/commit-graph.txt
index c664acbd765d06..18948f11a77256 100644
--- a/Documentation/technical/commit-graph.txt
+++ b/Documentation/technical/commit-graph.txt
@@ -112,12 +112,24 @@ Design Details
 - The file format includes parameters for the object ID hash function,
   so a future change of hash algorithm does not require a change in format.
 
+- Commit grafts and replace objects can change the shape of the commit
+  history. These can also be enabled/disabled on the fly using
+  `--no-replace-objects`. This leads to difficultly storing both possible
+  interpretations of a commit id, especially when computing generation
+  numbers. The commit-graph will not be read or written when
+  replace-objects or grafts are present.
+
+- Shallow clones create grafts of commits by dropping their parents. This
+  leads the commit-graph to think those commits have generation number 1.
+  If and when those commits are made unshallow, those generation numbers
+  become invalid. Since shallow clones are intended to restrict the commit
+  history to a very small set of commits, the commit-graph feature is less
+  helpful for these clones, anyway. The commit-graph will not be read or
+  written when shallow commits are present.
+
 Future Work
 -----------
 
-- The commit graph feature currently does not honor commit grafts. This can
-  be remedied by duplicating or refactoring the current graft logic.
-
 - After computing and storing generation numbers, we must make graph
   walks aware of generation numbers to gain the performance benefits they
   enable. This will mostly be accomplished by swapping a commit-date-ordered
diff --git a/commit-graph.c b/commit-graph.c
index b0a55ad128fbca..57310ab23d9543 100644
--- a/commit-graph.c
+++ b/commit-graph.c
@@ -13,6 +13,8 @@
 #include "commit-graph.h"
 #include "object-store.h"
 #include "alloc.h"
+#include "hashmap.h"
+#include "replace-object.h"
 
 #define GRAPH_SIGNATURE 0x43475048 /* "CGPH" */
 #define GRAPH_CHUNKID_OIDFANOUT 0x4f494446 /* "OIDF" */
@@ -56,6 +58,25 @@ static struct commit_graph *alloc_commit_graph(void)
 	return g;
 }
 
+static int commit_graph_compatible(struct repository *r)
+{
+	if (!r->gitdir)
+		return 0;
+
+	prepare_commit_graft(r);
+	if (r->parsed_objects && r->parsed_objects->grafts_nr)
+		return 0;
+	if (is_repository_shallow(r))
+		return 0;
+
+	prepare_replace_object(r);
+	if (check_replace_refs &&
+	    hashmap_get_size(&r->objects->replace_map->map))
+		return 0;
+
+	return 1;
+}
+
 struct commit_graph *load_commit_graph_one(const char *graph_file)
 {
 	void *graph_map;
@@ -223,6 +244,9 @@ static int prepare_commit_graph(struct repository *r)
 		 */
 		return 0;
 
+	if (!commit_graph_compatible(r))
+		return 0;
+
 	obj_dir = r->objects->objectdir;
 	prepare_commit_graph_one(r, obj_dir);
 	prepare_alt_odb(r);
@@ -233,10 +257,10 @@ static int prepare_commit_graph(struct repository *r)
 	return !!r->objects->commit_graph;
 }
 
-static void close_commit_graph(void)
+void close_commit_graph(struct repository *r)
 {
-	free_commit_graph(the_repository->objects->commit_graph);
-	the_repository->objects->commit_graph = NULL;
+	free_commit_graph(r->objects->commit_graph);
+	r->objects->commit_graph = NULL;
 }
 
 static int bsearch_graph(struct commit_graph *g, struct object_id *oid, uint32_t *pos)
@@ -693,6 +717,9 @@ void write_commit_graph(const char *obj_dir,
 	int num_extra_edges;
 	struct commit_list *parent;
 
+	if (!commit_graph_compatible(the_repository))
+		return;
+
 	oids.nr = 0;
 	oids.alloc = approximate_object_count() / 4;
 
@@ -845,7 +872,7 @@ void write_commit_graph(const char *obj_dir,
 	write_graph_chunk_data(f, GRAPH_OID_LEN, commits.list, commits.nr);
 	write_graph_chunk_large_edges(f, commits.list, commits.nr);
 
-	close_commit_graph();
+	close_commit_graph(the_repository);
 	finalize_hashfile(f, NULL, CSUM_HASH_IN_STREAM | CSUM_FSYNC);
 	commit_lock_file(&lk);
 
diff --git a/commit-graph.h b/commit-graph.h
index 76e098934a7f67..13d736cdde2898 100644
--- a/commit-graph.h
+++ b/commit-graph.h
@@ -59,6 +59,7 @@ void write_commit_graph(const char *obj_dir,
 
 int verify_commit_graph(struct repository *r, struct commit_graph *g);
 
+void close_commit_graph(struct repository *);
 void free_commit_graph(struct commit_graph *);
 
 #endif
diff --git a/commit.c b/commit.c
index 39b80bd21d59ca..609adaf8ad7b9c 100644
--- a/commit.c
+++ b/commit.c
@@ -209,7 +209,7 @@ static int read_graft_file(struct repository *r, const char *graft_file)
 	return 0;
 }
 
-static void prepare_commit_graft(struct repository *r)
+void prepare_commit_graft(struct repository *r)
 {
 	char *graft_file;
 
diff --git a/commit.h b/commit.h
index da0db36eba2bf1..5459e279fe02ae 100644
--- a/commit.h
+++ b/commit.h
@@ -202,6 +202,7 @@ typedef int (*each_commit_graft_fn)(const struct commit_graft *, void *);
 
 struct commit_graft *read_graft_line(struct strbuf *line);
 int register_commit_graft(struct repository *r, struct commit_graft *, int);
+void prepare_commit_graft(struct repository *r);
 struct commit_graft *lookup_commit_graft(struct repository *r, const struct object_id *oid);
 
 extern struct commit_list *get_merge_bases(struct commit *rev1, struct commit *rev2);
diff --git a/replace-object.c b/replace-object.c
index 801b5c16789f5a..6f6e707d177762 100644
--- a/replace-object.c
+++ b/replace-object.c
@@ -14,6 +14,7 @@ static int register_replace_ref(const char *refname,
 	const char *slash = strrchr(refname, '/');
 	const char *hash = slash ? slash + 1 : refname;
 	struct replace_object *repl_obj = xmalloc(sizeof(*repl_obj));
+	struct repository *r = (struct repository *)cb_data;
 
 	if (get_oid_hex(hash, &repl_obj->original.oid)) {
 		free(repl_obj);
@@ -25,13 +26,13 @@ static int register_replace_ref(const char *refname,
 	oidcpy(&repl_obj->replacement, oid);
 
 	/* Register new object */
-	if (oidmap_put(the_repository->objects->replace_map, repl_obj))
+	if (oidmap_put(r->objects->replace_map, repl_obj))
 		die("duplicate replace ref: %s", refname);
 
 	return 0;
 }
 
-static void prepare_replace_object(struct repository *r)
+void prepare_replace_object(struct repository *r)
 {
 	if (r->objects->replace_map)
 		return;
@@ -40,7 +41,7 @@ static void prepare_replace_object(struct repository *r)
 		xmalloc(sizeof(*r->objects->replace_map));
 	oidmap_init(r->objects->replace_map, 0);
 
-	for_each_replace_ref(r, register_replace_ref, NULL);
+	for_each_replace_ref(r, register_replace_ref, r);
 }
 
 /* We allow "recursive" replacement. Only within reason, though */
diff --git a/replace-object.h b/replace-object.h
index f996de3d62c6aa..c7a99fc35513ae 100644
--- a/replace-object.h
+++ b/replace-object.h
@@ -10,6 +10,8 @@ struct replace_object {
 	struct object_id replacement;
 };
 
+void prepare_replace_object(struct repository *r);
+
 /*
  * This internal function is only declared here for the benefit of
  * lookup_replace_object().  Please do not call it directly.
diff --git a/t/helper/test-repository.c b/t/helper/test-repository.c
index 2762ca656262ba..6a84a53efbf691 100644
--- a/t/helper/test-repository.c
+++ b/t/helper/test-repository.c
@@ -15,7 +15,10 @@ static void test_parse_commit_in_graph(const char *gitdir, const char *worktree,
 	struct commit *c;
 	struct commit_list *parent;
 
-	repo_init(&r, gitdir, worktree);
+	setup_git_env(gitdir);
+
+	if (repo_init(&r, gitdir, worktree))
+		die("Couldn't init repo");
 
 	c = lookup_commit(&r, commit_oid);
 
@@ -38,7 +41,10 @@ static void test_get_commit_tree_in_graph(const char *gitdir,
 	struct commit *c;
 	struct tree *tree;
 
-	repo_init(&r, gitdir, worktree);
+	setup_git_env(gitdir);
+
+	if (repo_init(&r, gitdir, worktree))
+		die("Couldn't init repo");
 
 	c = lookup_commit(&r, commit_oid);
 
diff --git a/t/t5318-commit-graph.sh b/t/t5318-commit-graph.sh
index 4f17d7701e456b..1d9f49af55fe83 100755
--- a/t/t5318-commit-graph.sh
+++ b/t/t5318-commit-graph.sh
@@ -259,6 +259,64 @@ test_expect_success 'check that gc computes commit-graph' '
 	test_cmp commit-graph-after-gc $objdir/info/commit-graph
 '
 
+test_expect_success 'replace-objects invalidates commit-graph' '
+	cd "$TRASH_DIRECTORY" &&
+	test_when_finished rm -rf replace &&
+	git clone full replace &&
+	(
+		cd replace &&
+		git commit-graph write --reachable &&
+		test_path_is_file .git/objects/info/commit-graph &&
+		git replace HEAD~1 HEAD~2 &&
+		git -c core.commitGraph=false log >expect &&
+		git -c core.commitGraph=true log >actual &&
+		test_cmp expect actual &&
+		git commit-graph write --reachable &&
+		git -c core.commitGraph=false --no-replace-objects log >expect &&
+		git -c core.commitGraph=true --no-replace-objects log >actual &&
+		test_cmp expect actual &&
+		rm -rf .git/objects/info/commit-graph &&
+		git commit-graph write --reachable &&
+		test_path_is_missing .git/objects/info/commit-graph
+	)
+'
+
+test_expect_success 'commit grafts invalidate commit-graph' '
+	cd "$TRASH_DIRECTORY" &&
+	test_when_finished rm -rf graft &&
+	git clone full graft &&
+	(
+		cd graft &&
+		git commit-graph write --reachable &&
+		test_path_is_file .git/objects/info/commit-graph &&
+		git replace --graft HEAD~1 HEAD~3 &&
+		git -c core.commitGraph=false log >expect &&
+		git -c core.commitGraph=true log >actual &&
+		test_cmp expect actual &&
+		git commit-graph write --reachable &&
+		git -c core.commitGraph=false --no-replace-objects log >expect &&
+		git -c core.commitGraph=true --no-replace-objects log >actual &&
+		test_cmp expect actual &&
+		rm -rf .git/objects/info/commit-graph &&
+		git commit-graph write --reachable &&
+		test_path_is_missing .git/objects/info/commit-graph
+	)
+'
+
+test_expect_success 'replace-objects invalidates commit-graph' '
+	cd "$TRASH_DIRECTORY" &&
+	test_when_finished rm -rf shallow &&
+	git clone --depth 2 "file://$TRASH_DIRECTORY/full" shallow &&
+	(
+		cd shallow &&
+		git commit-graph write --reachable &&
+		test_path_is_missing .git/objects/info/commit-graph &&
+		git fetch origin --unshallow &&
+		git commit-graph write --reachable &&
+		test_path_is_file .git/objects/info/commit-graph
+	)
+'
+
 # the verify tests below expect the commit-graph to contain
 # exactly the commits reachable from the commits/8 branch.
 # If the file changes the set of commits in the list, then the
diff --git a/upload-pack.c b/upload-pack.c
index 4ca052d0b64184..52ad6c8e5fc36e 100644
--- a/upload-pack.c
+++ b/upload-pack.c
@@ -24,6 +24,7 @@
 #include "quote.h"
 #include "upload-pack.h"
 #include "serve.h"
+#include "commit-graph.h"
 
 /* Remember to update object flag allocation in object.h */
 #define THEY_HAVE	(1u << 11)
@@ -739,6 +740,7 @@ static void deepen_by_rev_list(int ac, const char **av,
 {
 	struct commit_list *result;
 
+	close_commit_graph(the_repository);
 	result = get_shallow_commits_by_rev_list(ac, av, SHALLOW, NOT_SHALLOW);
 	send_shallow(result);
 	free_commit_list(result);