diff --git a/Makefile b/Makefile
index c3565fc0f8..a1525978fb 100644
--- a/Makefile
+++ b/Makefile
@@ -722,6 +722,7 @@ TEST_BUILTINS_OBJS += test-mergesort.o
 TEST_BUILTINS_OBJS += test-mktemp.o
 TEST_BUILTINS_OBJS += test-oid-array.o
 TEST_BUILTINS_OBJS += test-oidmap.o
+TEST_BUILTINS_OBJS += test-oidtree.o
 TEST_BUILTINS_OBJS += test-online-cpus.o
 TEST_BUILTINS_OBJS += test-parse-options.o
 TEST_BUILTINS_OBJS += test-parse-pathspec-file.o
@@ -845,6 +846,7 @@ LIB_OBJS += branch.o
 LIB_OBJS += bulk-checkin.o
 LIB_OBJS += bundle.o
 LIB_OBJS += cache-tree.o
+LIB_OBJS += cbtree.o
 LIB_OBJS += chdir-notify.o
 LIB_OBJS += checkout.o
 LIB_OBJS += chunk-format.o
@@ -940,6 +942,7 @@ LIB_OBJS += object.o
 LIB_OBJS += oid-array.o
 LIB_OBJS += oidmap.o
 LIB_OBJS += oidset.o
+LIB_OBJS += oidtree.o
 LIB_OBJS += pack-bitmap-write.o
 LIB_OBJS += pack-bitmap.o
 LIB_OBJS += pack-check.o
diff --git a/cbtree.c b/cbtree.c
new file mode 100644
index 0000000000..b0c65d810f
--- /dev/null
+++ b/cbtree.c
@@ -0,0 +1,167 @@
+/*
+ * crit-bit tree implementation, does no allocations internally
+ * For more information on crit-bit trees: https://cr.yp.to/critbit.html
+ * Based on Adam Langley's adaptation of Dan Bernstein's public domain code
+ * git clone https://github.com/agl/critbit.git
+ */
+#include "cbtree.h"
+
+static struct cb_node *cb_node_of(const void *p)
+{
+	return (struct cb_node *)((uintptr_t)p - 1);
+}
+
+/* locate the best match, does not do a final comparision */
+static struct cb_node *cb_internal_best_match(struct cb_node *p,
+					const uint8_t *k, size_t klen)
+{
+	while (1 & (uintptr_t)p) {
+		struct cb_node *q = cb_node_of(p);
+		uint8_t c = q->byte < klen ? k[q->byte] : 0;
+		size_t direction = (1 + (q->otherbits | c)) >> 8;
+
+		p = q->child[direction];
+	}
+	return p;
+}
+
+/* returns NULL if successful, existing cb_node if duplicate */
+struct cb_node *cb_insert(struct cb_tree *t, struct cb_node *node, size_t klen)
+{
+	size_t newbyte, newotherbits;
+	uint8_t c;
+	int newdirection;
+	struct cb_node **wherep, *p;
+
+	assert(!((uintptr_t)node & 1)); /* allocations must be aligned */
+
+	if (!t->root) {		/* insert into empty tree */
+		t->root = node;
+		return NULL;	/* success */
+	}
+
+	/* see if a node already exists */
+	p = cb_internal_best_match(t->root, node->k, klen);
+
+	/* find first differing byte */
+	for (newbyte = 0; newbyte < klen; newbyte++) {
+		if (p->k[newbyte] != node->k[newbyte])
+			goto different_byte_found;
+	}
+	return p;	/* element exists, let user deal with it */
+
+different_byte_found:
+	newotherbits = p->k[newbyte] ^ node->k[newbyte];
+	newotherbits |= newotherbits >> 1;
+	newotherbits |= newotherbits >> 2;
+	newotherbits |= newotherbits >> 4;
+	newotherbits = (newotherbits & ~(newotherbits >> 1)) ^ 255;
+	c = p->k[newbyte];
+	newdirection = (1 + (newotherbits | c)) >> 8;
+
+	node->byte = newbyte;
+	node->otherbits = newotherbits;
+	node->child[1 - newdirection] = node;
+
+	/* find a place to insert it */
+	wherep = &t->root;
+	for (;;) {
+		struct cb_node *q;
+		size_t direction;
+
+		p = *wherep;
+		if (!(1 & (uintptr_t)p))
+			break;
+		q = cb_node_of(p);
+		if (q->byte > newbyte)
+			break;
+		if (q->byte == newbyte && q->otherbits > newotherbits)
+			break;
+		c = q->byte < klen ? node->k[q->byte] : 0;
+		direction = (1 + (q->otherbits | c)) >> 8;
+		wherep = q->child + direction;
+	}
+
+	node->child[newdirection] = *wherep;
+	*wherep = (struct cb_node *)(1 + (uintptr_t)node);
+
+	return NULL; /* success */
+}
+
+struct cb_node *cb_lookup(struct cb_tree *t, const uint8_t *k, size_t klen)
+{
+	struct cb_node *p = cb_internal_best_match(t->root, k, klen);
+
+	return p && !memcmp(p->k, k, klen) ? p : NULL;
+}
+
+struct cb_node *cb_unlink(struct cb_tree *t, const uint8_t *k, size_t klen)
+{
+	struct cb_node **wherep = &t->root;
+	struct cb_node **whereq = NULL;
+	struct cb_node *q = NULL;
+	size_t direction = 0;
+	uint8_t c;
+	struct cb_node *p = t->root;
+
+	if (!p) return NULL;	/* empty tree, nothing to delete */
+
+	/* traverse to find best match, keeping link to parent */
+	while (1 & (uintptr_t)p) {
+		whereq = wherep;
+		q = cb_node_of(p);
+		c = q->byte < klen ? k[q->byte] : 0;
+		direction = (1 + (q->otherbits | c)) >> 8;
+		wherep = q->child + direction;
+		p = *wherep;
+	}
+
+	if (memcmp(p->k, k, klen))
+		return NULL;		/* no match, nothing unlinked */
+
+	/* found an exact match */
+	if (whereq)	/* update parent */
+		*whereq = q->child[1 - direction];
+	else
+		t->root = NULL;
+	return p;
+}
+
+static enum cb_next cb_descend(struct cb_node *p, cb_iter fn, void *arg)
+{
+	if (1 & (uintptr_t)p) {
+		struct cb_node *q = cb_node_of(p);
+		enum cb_next n = cb_descend(q->child[0], fn, arg);
+
+		return n == CB_BREAK ? n : cb_descend(q->child[1], fn, arg);
+	} else {
+		return fn(p, arg);
+	}
+}
+
+void cb_each(struct cb_tree *t, const uint8_t *kpfx, size_t klen,
+			cb_iter fn, void *arg)
+{
+	struct cb_node *p = t->root;
+	struct cb_node *top = p;
+	size_t i = 0;
+
+	if (!p) return; /* empty tree */
+
+	/* Walk tree, maintaining top pointer */
+	while (1 & (uintptr_t)p) {
+		struct cb_node *q = cb_node_of(p);
+		uint8_t c = q->byte < klen ? kpfx[q->byte] : 0;
+		size_t direction = (1 + (q->otherbits | c)) >> 8;
+
+		p = q->child[direction];
+		if (q->byte < klen)
+			top = p;
+	}
+
+	for (i = 0; i < klen; i++) {
+		if (p->k[i] != kpfx[i])
+			return; /* "best" match failed */
+	}
+	cb_descend(top, fn, arg);
+}
diff --git a/cbtree.h b/cbtree.h
new file mode 100644
index 0000000000..fe4587087e
--- /dev/null
+++ b/cbtree.h
@@ -0,0 +1,56 @@
+/*
+ * crit-bit tree implementation, does no allocations internally
+ * For more information on crit-bit trees: https://cr.yp.to/critbit.html
+ * Based on Adam Langley's adaptation of Dan Bernstein's public domain code
+ * git clone https://github.com/agl/critbit.git
+ *
+ * This is adapted to store arbitrary data (not just NUL-terminated C strings
+ * and allocates no memory internally.  The user needs to allocate
+ * "struct cb_node" and fill cb_node.k[] with arbitrary match data
+ * for memcmp.
+ * If "klen" is variable, then it should be embedded into "c_node.k[]"
+ * Recursion is bound by the maximum value of "klen" used.
+ */
+#ifndef CBTREE_H
+#define CBTREE_H
+
+#include "git-compat-util.h"
+
+struct cb_node;
+struct cb_node {
+	struct cb_node *child[2];
+	/*
+	 * n.b. uint32_t for `byte' is excessive for OIDs,
+	 * we may consider shorter variants if nothing else gets stored.
+	 */
+	uint32_t byte;
+	uint8_t otherbits;
+	uint8_t k[FLEX_ARRAY]; /* arbitrary data */
+};
+
+struct cb_tree {
+	struct cb_node *root;
+};
+
+enum cb_next {
+	CB_CONTINUE = 0,
+	CB_BREAK = 1
+};
+
+#define CBTREE_INIT { .root = NULL }
+
+static inline void cb_init(struct cb_tree *t)
+{
+	t->root = NULL;
+}
+
+struct cb_node *cb_lookup(struct cb_tree *, const uint8_t *k, size_t klen);
+struct cb_node *cb_insert(struct cb_tree *, struct cb_node *, size_t klen);
+struct cb_node *cb_unlink(struct cb_tree *t, const uint8_t *k, size_t klen);
+
+typedef enum cb_next (*cb_iter)(struct cb_node *, void *arg);
+
+void cb_each(struct cb_tree *, const uint8_t *kpfx, size_t klen,
+		cb_iter, void *arg);
+
+#endif /* CBTREE_H */
diff --git a/object-file.c b/object-file.c
index 91ded8c22a..35f3e7e9bb 100644
--- a/object-file.c
+++ b/object-file.c
@@ -1173,7 +1173,7 @@ static int quick_has_loose(struct repository *r,
 
 	prepare_alt_odb(r);
 	for (odb = r->objects->odb; odb; odb = odb->next) {
-		if (oid_array_lookup(odb_loose_cache(odb, oid), oid) >= 0)
+		if (oidtree_contains(odb_loose_cache(odb, oid), oid))
 			return 1;
 	}
 	return 0;
@@ -2452,11 +2452,11 @@ int for_each_loose_object(each_loose_object_fn cb, void *data,
 static int append_loose_object(const struct object_id *oid, const char *path,
 			       void *data)
 {
-	oid_array_append(data, oid);
+	oidtree_insert(data, oid);
 	return 0;
 }
 
-struct oid_array *odb_loose_cache(struct object_directory *odb,
+struct oidtree *odb_loose_cache(struct object_directory *odb,
 				  const struct object_id *oid)
 {
 	int subdir_nr = oid->hash[0];
@@ -2472,24 +2472,25 @@ struct oid_array *odb_loose_cache(struct object_directory *odb,
 
 	bitmap = &odb->loose_objects_subdir_seen[word_index];
 	if (*bitmap & mask)
-		return &odb->loose_objects_cache[subdir_nr];
-
+		return odb->loose_objects_cache;
+	if (!odb->loose_objects_cache) {
+		ALLOC_ARRAY(odb->loose_objects_cache, 1);
+		oidtree_init(odb->loose_objects_cache);
+	}
 	strbuf_addstr(&buf, odb->path);
 	for_each_file_in_obj_subdir(subdir_nr, &buf,
 				    append_loose_object,
 				    NULL, NULL,
-				    &odb->loose_objects_cache[subdir_nr]);
+				    odb->loose_objects_cache);
 	*bitmap |= mask;
 	strbuf_release(&buf);
-	return &odb->loose_objects_cache[subdir_nr];
+	return odb->loose_objects_cache;
 }
 
 void odb_clear_loose_cache(struct object_directory *odb)
 {
-	int i;
-
-	for (i = 0; i < ARRAY_SIZE(odb->loose_objects_cache); i++)
-		oid_array_clear(&odb->loose_objects_cache[i]);
+	oidtree_clear(odb->loose_objects_cache);
+	FREE_AND_NULL(odb->loose_objects_cache);
 	memset(&odb->loose_objects_subdir_seen, 0,
 	       sizeof(odb->loose_objects_subdir_seen));
 }
diff --git a/object-name.c b/object-name.c
index 64202de60b..3263c19457 100644
--- a/object-name.c
+++ b/object-name.c
@@ -87,27 +87,21 @@ static void update_candidates(struct disambiguate_state *ds, const struct object
 
 static int match_hash(unsigned, const unsigned char *, const unsigned char *);
 
+static enum cb_next match_prefix(const struct object_id *oid, void *arg)
+{
+	struct disambiguate_state *ds = arg;
+	/* no need to call match_hash, oidtree_each did prefix match */
+	update_candidates(ds, oid);
+	return ds->ambiguous ? CB_BREAK : CB_CONTINUE;
+}
+
 static void find_short_object_filename(struct disambiguate_state *ds)
 {
 	struct object_directory *odb;
 
-	for (odb = ds->repo->objects->odb; odb && !ds->ambiguous; odb = odb->next) {
-		int pos;
-		struct oid_array *loose_objects;
-
-		loose_objects = odb_loose_cache(odb, &ds->bin_pfx);
-		pos = oid_array_lookup(loose_objects, &ds->bin_pfx);
-		if (pos < 0)
-			pos = -1 - pos;
-		while (!ds->ambiguous && pos < loose_objects->nr) {
-			const struct object_id *oid;
-			oid = loose_objects->oid + pos;
-			if (!match_hash(ds->len, ds->bin_pfx.hash, oid->hash))
-				break;
-			update_candidates(ds, oid);
-			pos++;
-		}
-	}
+	for (odb = ds->repo->objects->odb; odb && !ds->ambiguous; odb = odb->next)
+		oidtree_each(odb_loose_cache(odb, &ds->bin_pfx),
+				&ds->bin_pfx, ds->len, match_prefix, ds);
 }
 
 static int match_hash(unsigned len, const unsigned char *a, const unsigned char *b)
diff --git a/object-store.h b/object-store.h
index ab6d469970..e679acc4c3 100644
--- a/object-store.h
+++ b/object-store.h
@@ -9,6 +9,7 @@
 #include "thread-utils.h"
 #include "khash.h"
 #include "dir.h"
+#include "oidtree.h"
 
 struct object_directory {
 	struct object_directory *next;
@@ -23,7 +24,7 @@ struct object_directory {
 	 * Be sure to call odb_load_loose_cache() before using.
 	 */
 	uint32_t loose_objects_subdir_seen[8]; /* 256 bits */
-	struct oid_array loose_objects_cache[256];
+	struct oidtree *loose_objects_cache;
 
 	/*
 	 * Path to the alternative object store. If this is a relative path,
@@ -59,7 +60,7 @@ void add_to_alternates_memory(const char *dir);
  * Populate and return the loose object cache array corresponding to the
  * given object ID.
  */
-struct oid_array *odb_loose_cache(struct object_directory *odb,
+struct oidtree *odb_loose_cache(struct object_directory *odb,
 				  const struct object_id *oid);
 
 /* Empty the loose object cache for the specified object directory. */
diff --git a/oidtree.c b/oidtree.c
new file mode 100644
index 0000000000..7eb0e9ba05
--- /dev/null
+++ b/oidtree.c
@@ -0,0 +1,104 @@
+/*
+ * A wrapper around cbtree which stores oids
+ * May be used to replace oid-array for prefix (abbreviation) matches
+ */
+#include "oidtree.h"
+#include "alloc.h"
+#include "hash.h"
+
+struct oidtree_node {
+	/* n.k[] is used to store "struct object_id" */
+	struct cb_node n;
+};
+
+struct oidtree_iter_data {
+	oidtree_iter fn;
+	void *arg;
+	size_t *last_nibble_at;
+	int algo;
+	uint8_t last_byte;
+};
+
+void oidtree_init(struct oidtree *ot)
+{
+	cb_init(&ot->tree);
+	mem_pool_init(&ot->mem_pool, 0);
+}
+
+void oidtree_clear(struct oidtree *ot)
+{
+	if (ot) {
+		mem_pool_discard(&ot->mem_pool, 0);
+		oidtree_init(ot);
+	}
+}
+
+void oidtree_insert(struct oidtree *ot, const struct object_id *oid)
+{
+	struct oidtree_node *on;
+
+	if (!oid->algo)
+		BUG("oidtree_insert requires oid->algo");
+
+	on = mem_pool_alloc(&ot->mem_pool, sizeof(*on) + sizeof(*oid));
+	oidcpy_with_padding((struct object_id *)on->n.k, oid);
+
+	/*
+	 * n.b. Current callers won't get us duplicates, here.  If a
+	 * future caller causes duplicates, there'll be a a small leak
+	 * that won't be freed until oidtree_clear.  Currently it's not
+	 * worth maintaining a free list
+	 */
+	cb_insert(&ot->tree, &on->n, sizeof(*oid));
+}
+
+
+int oidtree_contains(struct oidtree *ot, const struct object_id *oid)
+{
+	struct object_id k;
+	size_t klen = sizeof(k);
+
+	oidcpy_with_padding(&k, oid);
+
+	if (oid->algo == GIT_HASH_UNKNOWN)
+		klen -= sizeof(oid->algo);
+
+	/* cb_lookup relies on memcmp on the struct, so order matters: */
+	klen += BUILD_ASSERT_OR_ZERO(offsetof(struct object_id, hash) <
+				offsetof(struct object_id, algo));
+
+	return cb_lookup(&ot->tree, (const uint8_t *)&k, klen) ? 1 : 0;
+}
+
+static enum cb_next iter(struct cb_node *n, void *arg)
+{
+	struct oidtree_iter_data *x = arg;
+	const struct object_id *oid = (const struct object_id *)n->k;
+
+	if (x->algo != GIT_HASH_UNKNOWN && x->algo != oid->algo)
+		return CB_CONTINUE;
+
+	if (x->last_nibble_at) {
+		if ((oid->hash[*x->last_nibble_at] ^ x->last_byte) & 0xf0)
+			return CB_CONTINUE;
+	}
+
+	return x->fn(oid, x->arg);
+}
+
+void oidtree_each(struct oidtree *ot, const struct object_id *oid,
+			size_t oidhexsz, oidtree_iter fn, void *arg)
+{
+	size_t klen = oidhexsz / 2;
+	struct oidtree_iter_data x = { 0 };
+	assert(oidhexsz <= GIT_MAX_HEXSZ);
+
+	x.fn = fn;
+	x.arg = arg;
+	x.algo = oid->algo;
+	if (oidhexsz & 1) {
+		x.last_byte = oid->hash[klen];
+		x.last_nibble_at = &klen;
+	}
+	cb_each(&ot->tree, (const uint8_t *)oid, klen, iter, &x);
+}
diff --git a/oidtree.h b/oidtree.h
new file mode 100644
index 0000000000..77898f510a
--- /dev/null
+++ b/oidtree.h
@@ -0,0 +1,22 @@
+#ifndef OIDTREE_H
+#define OIDTREE_H
+
+#include "cbtree.h"
+#include "hash.h"
+#include "mem-pool.h"
+
+struct oidtree {
+	struct cb_tree tree;
+	struct mem_pool mem_pool;
+};
+
+void oidtree_init(struct oidtree *);
+void oidtree_clear(struct oidtree *);
+void oidtree_insert(struct oidtree *, const struct object_id *);
+int oidtree_contains(struct oidtree *, const struct object_id *);
+
+typedef enum cb_next (*oidtree_iter)(const struct object_id *, void *data);
+void oidtree_each(struct oidtree *, const struct object_id *,
+			size_t oidhexsz, oidtree_iter, void *data);
+
+#endif /* OIDTREE_H */
diff --git a/t/helper/test-oidtree.c b/t/helper/test-oidtree.c
new file mode 100644
index 0000000000..180ee28dd9
--- /dev/null
+++ b/t/helper/test-oidtree.c
@@ -0,0 +1,49 @@
+#include "test-tool.h"
+#include "cache.h"
+#include "oidtree.h"
+
+static enum cb_next print_oid(const struct object_id *oid, void *data)
+{
+	puts(oid_to_hex(oid));
+	return CB_CONTINUE;
+}
+
+int cmd__oidtree(int argc, const char **argv)
+{
+	struct oidtree ot;
+	struct strbuf line = STRBUF_INIT;
+	int nongit_ok;
+	int algo = GIT_HASH_UNKNOWN;
+
+	oidtree_init(&ot);
+	setup_git_directory_gently(&nongit_ok);
+
+	while (strbuf_getline(&line, stdin) != EOF) {
+		const char *arg;
+		struct object_id oid;
+
+		if (skip_prefix(line.buf, "insert ", &arg)) {
+			if (get_oid_hex_any(arg, &oid) == GIT_HASH_UNKNOWN)
+				die("insert not a hexadecimal oid: %s", arg);
+			algo = oid.algo;
+			oidtree_insert(&ot, &oid);
+		} else if (skip_prefix(line.buf, "contains ", &arg)) {
+			if (get_oid_hex(arg, &oid))
+				die("contains not a hexadecimal oid: %s", arg);
+			printf("%d\n", oidtree_contains(&ot, &oid));
+		} else if (skip_prefix(line.buf, "each ", &arg)) {
+			char buf[GIT_MAX_HEXSZ + 1] = { '0' };
+			memset(&oid, 0, sizeof(oid));
+			memcpy(buf, arg, strlen(arg));
+			buf[hash_algos[algo].hexsz] = '\0';
+			get_oid_hex_any(buf, &oid);
+			oid.algo = algo;
+			oidtree_each(&ot, &oid, strlen(arg), print_oid, NULL);
+		} else if (!strcmp(line.buf, "clear")) {
+			oidtree_clear(&ot);
+		} else {
+			die("unknown command: %s", line.buf);
+		}
+	}
+	return 0;
+}
diff --git a/t/helper/test-tool.c b/t/helper/test-tool.c
index c5bd0c6d4c..9d37debf28 100644
--- a/t/helper/test-tool.c
+++ b/t/helper/test-tool.c
@@ -43,6 +43,7 @@ static struct test_cmd cmds[] = {
 	{ "mktemp", cmd__mktemp },
 	{ "oid-array", cmd__oid_array },
 	{ "oidmap", cmd__oidmap },
+	{ "oidtree", cmd__oidtree },
 	{ "online-cpus", cmd__online_cpus },
 	{ "parse-options", cmd__parse_options },
 	{ "parse-pathspec-file", cmd__parse_pathspec_file },
diff --git a/t/helper/test-tool.h b/t/helper/test-tool.h
index e8069a3b22..f683a2f59c 100644
--- a/t/helper/test-tool.h
+++ b/t/helper/test-tool.h
@@ -32,6 +32,7 @@ int cmd__match_trees(int argc, const char **argv);
 int cmd__mergesort(int argc, const char **argv);
 int cmd__mktemp(int argc, const char **argv);
 int cmd__oidmap(int argc, const char **argv);
+int cmd__oidtree(int argc, const char **argv);
 int cmd__online_cpus(int argc, const char **argv);
 int cmd__parse_options(int argc, const char **argv);
 int cmd__parse_pathspec_file(int argc, const char** argv);
diff --git a/t/t0069-oidtree.sh b/t/t0069-oidtree.sh
new file mode 100755
index 0000000000..bfb1397d7b
--- /dev/null
+++ b/t/t0069-oidtree.sh
@@ -0,0 +1,49 @@
+#!/bin/sh
+
+test_description='basic tests for the oidtree implementation'
+. ./test-lib.sh
+
+maxhexsz=$(test_oid hexsz)
+echoid () {
+	prefix="${1:+$1 }"
+	shift
+	while test $# -gt 0
+	do
+		shortoid="$1"
+		shift
+		difference=$(($maxhexsz - ${#shortoid}))
+		printf "%s%s%0${difference}d\\n" "$prefix" "$shortoid" "0"
+	done
+}
+
+test_expect_success 'oidtree insert and contains' '
+	cat >expect <<-\EOF &&
+		0
+		0
+		0
+		1
+		1
+		0
+	EOF
+	{
+		echoid insert 444 1 2 3 4 5 a b c d e &&
+		echoid contains 44 441 440 444 4440 4444
+		echo clear
+	} | test-tool oidtree >actual &&
+	test_cmp expect actual
+'
+
+test_expect_success 'oidtree each' '
+	echoid "" 123 321 321 >expect &&
+	{
+		echoid insert f 9 8 123 321 a b c d e
+		echo each 12300
+		echo each 3211
+		echo each 3210
+		echo each 32100
+		echo clear
+	} | test-tool oidtree >actual &&
+	test_cmp expect actual
+'
+
+test_done