diff --git a/src/generators/jsonSchema.js b/src/generators/jsonSchema.js
index f1b5e39..8d42c5b 100644
--- a/src/generators/jsonSchema.js
+++ b/src/generators/jsonSchema.js
@@ -1,6 +1,6 @@
 import wu from 'wu';
 
-import {invariant, collect} from '../utils';
+import {invariant, collect, partition} from '../utils';
 import type Fund from '../fund';
 import type {Type, NumberType} from '../types';
 
@@ -114,8 +114,29 @@ function convert(fund: Fund, type: ?Type): Schema {
                 anyOf: schemas,
             };
         case 'intersection':
-            return {
-                allOf: wu(type.parts).map(part => convert(fund, part)).toArray(),
+            const [maps, others] = partition(type.parts, type => type.kind === 'map');
+
+            const parts = wu(others).map(part => convert(fund, part)).toArray();
+
+            if (maps.length > 0) {
+                const keys = wu(maps).map(map => convert(fund, (map: $FlowFixMe).values)).toArray();
+                const key = keys.length === 1 ? keys[0] : {anyOf: keys};
+
+                if (parts.length === 1 && parts[0].type === 'object') {
+                    invariant(typeof parts[0] === 'object');
+                    invariant(parts[0].additionalProperties == null);
+
+                    parts[0].additionalProperties = key;
+                } else {
+                    parts.push({
+                        type: 'object',
+                        additionalProperties: key,
+                    });
+                }
+            }
+
+            return parts.length === 1 ? parts[0] : {
+                allOf: parts,
             };
         case 'maybe':
             return {
diff --git a/src/utils.js b/src/utils.js
index 2de1caf..01c9374 100644
--- a/src/utils.js
+++ b/src/utils.js
@@ -19,3 +19,13 @@ export function collect<T>(iter: Iterable<[string, T]>): {[string]: T} {
 
     return result;
 }
+
+export function partition<T>(iter: Iterable<T>, pred: T => boolean): [T[], T[]] {
+    const [left, right] = [[], []];
+
+    for (const item of iter) {
+        (pred(item) ? left : right).push(item);
+    }
+
+    return [left, right];
+}
diff --git a/tests/samples/maps/schema.json b/tests/samples/maps/schema.json
index 32cf48a..624a43c 100644
--- a/tests/samples/maps/schema.json
+++ b/tests/samples/maps/schema.json
@@ -10,20 +10,19 @@
             "additionalProperties": {"type": "boolean"}
         },
         "maps::Couple": {
-            "allOf": [
-                {"type": "object", "additionalProperties": {"type": "boolean"}},
-                {"type": "object", "additionalProperties": {"type": "string"}}
-            ]
+            "type":  "object",
+            "additionalProperties": {
+                "anyOf": [
+                    {"type": "boolean"},
+                    {"type": "string"}
+                ]
+            }
         },
         "maps::Mix": {
-            "allOf": [
-                {
-                    "type": "object",
-                    "properties": {"foo": {"type": "string"}},
-                    "required": ["foo"]
-                },
-                {"type": "object", "additionalProperties": {"type": "boolean"}}
-            ]
+            "type": "object",
+            "properties": {"foo": {"type": "string"}},
+            "required": ["foo"],
+            "additionalProperties": {"type": "boolean"}
         }
     }
 }