diff --git a/CHANGELOG.md b/CHANGELOG.md
index feea88a2a..e4f5c78a7 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -11,7 +11,8 @@
 > - [Experimental]
 > - [Deprecation]
 
-**Note**: Gaps between patch versions are faulty/broken releases. **Note**: A feature tagged as Experimental is in a
+**Note**: Gaps between patch versions are faulty/broken releases.
+**Note**: A feature tagged as Experimental is in a
 high state of flux, you're at risk of it changing without notice.
 
 # 2.7.1
@@ -23,10 +24,12 @@ high state of flux, you're at risk of it changing without notice.
 - **Polish**
   - `Array`
     - relax `sort` signature (@gcanti)
+    - relax `sortBy` signature (@gcanti)
   - `Map`
     - export `mapWithIndex` (@gcanti)
   - `ReadonlyArray`
     - relax `sort` signature (@gcanti)
+    - relax `sortBy` signature (@gcanti)
   - `ReadonlyMap`
     - export `mapWithIndex` (@gcanti)
 
diff --git a/docs/modules/Array.ts.md b/docs/modules/Array.ts.md
index ee81bd300..0d4ad42be 100644
--- a/docs/modules/Array.ts.md
+++ b/docs/modules/Array.ts.md
@@ -863,7 +863,7 @@ etc...
 **Signature**
 
 ```ts
-export declare const sortBy: <A>(ords: Ord<A>[]) => (as: A[]) => A[]
+export declare const sortBy: <B>(ords: Ord<B>[]) => <A extends B>(as: A[]) => A[]
 ```
 
 **Example**
diff --git a/docs/modules/ReadonlyArray.ts.md b/docs/modules/ReadonlyArray.ts.md
index 4e611f87c..0fea5e05f 100644
--- a/docs/modules/ReadonlyArray.ts.md
+++ b/docs/modules/ReadonlyArray.ts.md
@@ -863,7 +863,7 @@ etc...
 **Signature**
 
 ```ts
-export declare function sortBy<A>(ords: ReadonlyArray<Ord<A>>): (as: ReadonlyArray<A>) => ReadonlyArray<A>
+export declare function sortBy<B>(ords: ReadonlyArray<Ord<B>>): <A extends B>(as: ReadonlyArray<A>) => ReadonlyArray<A>
 ```
 
 **Example**
diff --git a/dtslint/ts3.5/Array.ts b/dtslint/ts3.5/Array.ts
index 320bf974e..ab2f8d416 100644
--- a/dtslint/ts3.5/Array.ts
+++ b/dtslint/ts3.5/Array.ts
@@ -1,6 +1,7 @@
 import * as _ from '../../src/Array'
 import { pipe } from '../../src/pipeable'
 import { eqNumber } from '../../src/Eq'
+import { Ord } from '../../src/Ord'
 
 declare const us: Array<unknown>
 declare const ns: Array<number>
@@ -133,3 +134,31 @@ _.zip(['a', 'b']) // $ExpectType <A>(as: A[]) => [A, string][]
 
 _.cons(0, [1, 2]) // $ExpectType NonEmptyArray<number>
 _.cons(0) // $ExpectType (tail: number[]) => NonEmptyArray<number>
+
+//
+// sort
+//
+
+declare const ord1: Ord<{ readonly a: string }>
+interface X1 {
+  readonly a: string
+  readonly b: number
+}
+declare const x1s: Array<X1>
+
+_.sort(ord1)(x1s) // $ExpectType X1[]
+
+//
+// sortBy
+//
+
+declare const ord2: Ord<X1>
+declare const ord3: Ord<X1>
+interface X2 {
+  readonly a: string
+  readonly b: number
+  readonly c: boolean
+}
+declare const x2s: Array<X2>
+
+_.sortBy([ord2, ord3])(x2s) // $ExpectType X2[]
diff --git a/dtslint/ts3.5/ReadonlyArray.ts b/dtslint/ts3.5/ReadonlyArray.ts
index cc6ffc525..d11f4b1ee 100644
--- a/dtslint/ts3.5/ReadonlyArray.ts
+++ b/dtslint/ts3.5/ReadonlyArray.ts
@@ -1,6 +1,7 @@
 import * as _ from '../../src/ReadonlyArray'
 import { pipe } from '../../src/pipeable'
 import { eqNumber } from '../../src/Eq'
+import { Ord } from '../../src/Ord'
 
 declare const rus: ReadonlyArray<unknown>
 declare const rns: ReadonlyArray<number>
@@ -124,3 +125,31 @@ _.zip(['a', 'b']) // $ExpectType <A>(as: readonly A[]) => readonly (readonly [A,
 
 _.cons(0, [1, 2]) // $ExpectType ReadonlyNonEmptyArray<number>
 _.cons(0) // $ExpectType (tail: readonly number[]) => ReadonlyNonEmptyArray<number>
+
+//
+// sort
+//
+
+declare const ord1: Ord<{ readonly a: string }>
+interface X1 {
+  readonly a: string
+  readonly b: number
+}
+declare const x1s: ReadonlyArray<X1>
+
+_.sort(ord1)(x1s) // $ExpectType ReadonlyArray<X1>
+
+//
+// sortBy
+//
+
+declare const ord2: Ord<X1>
+declare const ord3: Ord<X1>
+interface X2 {
+  readonly a: string
+  readonly b: number
+  readonly c: boolean
+}
+declare const x2s: ReadonlyArray<X2>
+
+_.sortBy([ord2, ord3])(x2s) // $ExpectType ReadonlyArray<X2>
diff --git a/src/Array.ts b/src/Array.ts
index 362ffbc61..eced21821 100644
--- a/src/Array.ts
+++ b/src/Array.ts
@@ -801,7 +801,7 @@ export const uniq: <A>(E: Eq<A>) => (as: Array<A>) => Array<A> = RA.uniq as any
  * @category combinators
  * @since 2.0.0
  */
-export const sortBy: <A>(ords: Array<Ord<A>>) => (as: Array<A>) => Array<A> = RA.sortBy as any
+export const sortBy: <B>(ords: Array<Ord<B>>) => <A extends B>(as: Array<A>) => Array<A> = RA.sortBy as any
 
 /**
  * A useful recursion pattern for processing an array to produce a new array, often used for "chopping" up the input
diff --git a/src/ReadonlyArray.ts b/src/ReadonlyArray.ts
index a518d6ece..9325e27f0 100644
--- a/src/ReadonlyArray.ts
+++ b/src/ReadonlyArray.ts
@@ -1170,8 +1170,8 @@ export function uniq<A>(E: Eq<A>): (as: ReadonlyArray<A>) => ReadonlyArray<A> {
  * @category combinators
  * @since 2.5.0
  */
-export function sortBy<A>(ords: ReadonlyArray<Ord<A>>): (as: ReadonlyArray<A>) => ReadonlyArray<A> {
-  const M = getOrdMonoid<A>()
+export function sortBy<B>(ords: ReadonlyArray<Ord<B>>): <A extends B>(as: ReadonlyArray<A>) => ReadonlyArray<A> {
+  const M = getOrdMonoid<B>()
   return sort(ords.reduce(M.concat, M.empty))
 }