diff --git a/src/util/map.js b/src/util/map.js
index f0865c9..23e167e 100644
--- a/src/util/map.js
+++ b/src/util/map.js
@@ -7,8 +7,8 @@
  */
 export function toObject<K: string, V, InK: K, InV: V>(
   map: Map<InK, InV>
-): {[K]: V} {
-  const result = {};
+): {|[K]: V|} {
+  const result: {|[K]: V|} = ({}: any);
   for (const [k, v] of map.entries()) {
     result[k] = v;
   }
diff --git a/src/util/map.test.js b/src/util/map.test.js
index 7c7ae50..070e954 100644
--- a/src/util/map.test.js
+++ b/src/util/map.test.js
@@ -17,6 +17,14 @@ describe("util/map", () => {
       const output: {[Fruit]: string} = MapUtil.toObject(input);
       expect(output).toEqual({APPLE: "good", ORANGE: "also good"});
     });
+    it("can return an exact object", () => {
+      const _: {|[string]: number|} = MapUtil.toObject(new Map().set("a", 1));
+    });
+    it("can return an inexact object", () => {
+      // This should be free: exact objects are subtypes of their
+      // inexact counterparts.
+      const _: {[string]: number} = MapUtil.toObject(new Map().set("a", 1));
+    });
     it("statically rejects a map with keys not a subtype of string", () => {
       const input: Map<number, string> = new Map()
         .set(12, "not okay")
@@ -53,6 +61,16 @@ describe("util/map", () => {
         new Map().set("APPLE", "good").set("ORANGE", "also good")
       );
     });
+    it("can accept an inexact object", () => {
+      const o: {[string]: number} = {a: 1};
+      const _: Map<string, number> = MapUtil.fromObject(o);
+    });
+    it("can accept an exact object", () => {
+      // This should be free: exact objects are subtypes of their
+      // inexact counterparts.
+      const o: {|[string]: number|} = ({a: 1}: any);
+      const _: Map<string, number> = MapUtil.fromObject(o);
+    });
     it("statically rejects a map with keys not a subtype of string", () => {
       const input: {[number]: string} = {};
       input[12] = "not okay";