diff --git a/src/compiler/checker.ts b/src/compiler/checker.ts
index 4c74b60766b..6385d150a3e 100644
--- a/src/compiler/checker.ts
+++ b/src/compiler/checker.ts
@@ -14574,7 +14574,12 @@ namespace ts {
                     priority |= InferencePriority.MappedTypeConstraint;
                     inferFromTypes(getIndexType(source), constraintType);
                     priority = savePriority;
-                    inferFromTypes(getUnionType(map(getPropertiesOfType(source), getTypeOfSymbol)), getTemplateTypeFromMappedType(<MappedType>target));
+                    const valueTypes = compact([
+                        getIndexTypeOfType(source, IndexKind.String),
+                        getIndexTypeOfType(source, IndexKind.Number),
+                        ...map(getPropertiesOfType(source), getTypeOfSymbol)
+                    ]);
+                    inferFromTypes(getUnionType(valueTypes), getTemplateTypeFromMappedType(<MappedType>target));
                     return true;
                 }
                 return false;
diff --git a/src/compiler/core.ts b/src/compiler/core.ts
index d4f5fe9664a..fd4807fc586 100644
--- a/src/compiler/core.ts
+++ b/src/compiler/core.ts
@@ -884,8 +884,11 @@ namespace ts {
     /**
      * Compacts an array, removing any falsey elements.
      */
-    export function compact<T>(array: T[]): T[];
-    export function compact<T>(array: ReadonlyArray<T>): ReadonlyArray<T>;
+    export function compact<T>(array: (T | undefined | null | false | 0 | "")[]): T[];
+    export function compact<T>(array: ReadonlyArray<T | undefined | null | false | 0 | "">): ReadonlyArray<T>;
+    // TSLint thinks these can be combined with the above - they cannot; they'd produce higher-priority inferences and prevent the falsey types from being stripped
+    export function compact<T>(array: T[]): T[]; // tslint:disable-line unified-signatures
+    export function compact<T>(array: ReadonlyArray<T>): ReadonlyArray<T>; // tslint:disable-line unified-signatures
     export function compact<T>(array: T[]): T[] {
         let result: T[] | undefined;
         if (array) {
diff --git a/tests/baselines/reference/mappedToToIndexSignatureInference.js b/tests/baselines/reference/mappedToToIndexSignatureInference.js
new file mode 100644
index 00000000000..2ea09b663a9
--- /dev/null
+++ b/tests/baselines/reference/mappedToToIndexSignatureInference.js
@@ -0,0 +1,8 @@
+//// [mappedToToIndexSignatureInference.ts]
+declare const fn: <K extends string, V>(object: { [Key in K]: V }) => object;
+declare const a: { [index: string]: number };
+fn(a);
+
+
+//// [mappedToToIndexSignatureInference.js]
+fn(a);
diff --git a/tests/baselines/reference/mappedToToIndexSignatureInference.symbols b/tests/baselines/reference/mappedToToIndexSignatureInference.symbols
new file mode 100644
index 00000000000..d071f3f4c1c
--- /dev/null
+++ b/tests/baselines/reference/mappedToToIndexSignatureInference.symbols
@@ -0,0 +1,18 @@
+=== tests/cases/compiler/mappedToToIndexSignatureInference.ts ===
+declare const fn: <K extends string, V>(object: { [Key in K]: V }) => object;
+>fn : Symbol(fn, Decl(mappedToToIndexSignatureInference.ts, 0, 13))
+>K : Symbol(K, Decl(mappedToToIndexSignatureInference.ts, 0, 19))
+>V : Symbol(V, Decl(mappedToToIndexSignatureInference.ts, 0, 36))
+>object : Symbol(object, Decl(mappedToToIndexSignatureInference.ts, 0, 40))
+>Key : Symbol(Key, Decl(mappedToToIndexSignatureInference.ts, 0, 51))
+>K : Symbol(K, Decl(mappedToToIndexSignatureInference.ts, 0, 19))
+>V : Symbol(V, Decl(mappedToToIndexSignatureInference.ts, 0, 36))
+
+declare const a: { [index: string]: number };
+>a : Symbol(a, Decl(mappedToToIndexSignatureInference.ts, 1, 13))
+>index : Symbol(index, Decl(mappedToToIndexSignatureInference.ts, 1, 20))
+
+fn(a);
+>fn : Symbol(fn, Decl(mappedToToIndexSignatureInference.ts, 0, 13))
+>a : Symbol(a, Decl(mappedToToIndexSignatureInference.ts, 1, 13))
+
diff --git a/tests/baselines/reference/mappedToToIndexSignatureInference.types b/tests/baselines/reference/mappedToToIndexSignatureInference.types
new file mode 100644
index 00000000000..35b9b3565e0
--- /dev/null
+++ b/tests/baselines/reference/mappedToToIndexSignatureInference.types
@@ -0,0 +1,14 @@
+=== tests/cases/compiler/mappedToToIndexSignatureInference.ts ===
+declare const fn: <K extends string, V>(object: { [Key in K]: V }) => object;
+>fn : <K extends string, V>(object: { [Key in K]: V; }) => object
+>object : { [Key in K]: V; }
+
+declare const a: { [index: string]: number };
+>a : { [index: string]: number; }
+>index : string
+
+fn(a);
+>fn(a) : object
+>fn : <K extends string, V>(object: { [Key in K]: V; }) => object
+>a : { [index: string]: number; }
+
diff --git a/tests/cases/compiler/mappedToToIndexSignatureInference.ts b/tests/cases/compiler/mappedToToIndexSignatureInference.ts
new file mode 100644
index 00000000000..6ce63ead59c
--- /dev/null
+++ b/tests/cases/compiler/mappedToToIndexSignatureInference.ts
@@ -0,0 +1,3 @@
+declare const fn: <K extends string, V>(object: { [Key in K]: V }) => object;
+declare const a: { [index: string]: number };
+fn(a);