diff --git a/cache-tree.c b/cache-tree.c
index 5f07a39e50..950a9615db 100644
--- a/cache-tree.c
+++ b/cache-tree.c
@@ -256,6 +256,24 @@ static int update_one(struct cache_tree *it,
 
 	*skip_count = 0;
 
+	/*
+	 * If the first entry of this region is a sparse directory
+	 * entry corresponding exactly to 'base', then this cache_tree
+	 * struct is a "leaf" in the data structure, pointing to the
+	 * tree OID specified in the entry.
+	 */
+	if (entries > 0) {
+		const struct cache_entry *ce = cache[0];
+
+		if (S_ISSPARSEDIR(ce->ce_mode) &&
+		    ce->ce_namelen == baselen &&
+		    !strncmp(ce->name, base, baselen)) {
+			it->entry_count = 1;
+			oidcpy(&it->oid, &ce->oid);
+			return 1;
+		}
+	}
+
 	if (0 <= it->entry_count && has_object_file(&it->oid))
 		return it->entry_count;
 
diff --git a/sparse-index.c b/sparse-index.c
index 4c73772c6d..95ea17174d 100644
--- a/sparse-index.c
+++ b/sparse-index.c
@@ -172,7 +172,11 @@ int convert_to_sparse(struct index_state *istate)
 	istate->cache_nr = convert_to_sparse_rec(istate,
 						 0, 0, istate->cache_nr,
 						 "", 0, istate->cache_tree);
-	istate->drop_cache_tree = 1;
+
+	/* Clear and recompute the cache-tree */
+	cache_tree_free(&istate->cache_tree);
+	cache_tree_update(istate, 0);
+
 	istate->sparse_index = 1;
 	trace2_region_leave("index", "convert_to_sparse", istate->repo);
 	return 0;
@@ -273,5 +277,9 @@ void ensure_full_index(struct index_state *istate)
 	strbuf_release(&base);
 	free(full);
 
+	/* Clear and recompute the cache-tree */
+	cache_tree_free(&istate->cache_tree);
+	cache_tree_update(istate, 0);
+
 	trace2_region_leave("index", "ensure_full_index", istate->repo);
 }