diff --git a/types/sinon/ts3.1/index.d.ts b/types/sinon/ts3.1/index.d.ts
index cab3c80b674777..6641d3510fc1ac 100644
--- a/types/sinon/ts3.1/index.d.ts
+++ b/types/sinon/ts3.1/index.d.ts
@@ -6,7 +6,9 @@ interface Document {} // tslint:disable-line no-empty-interface
 
 declare namespace Sinon {
     type MatchArguments<T> = {
-        [K in keyof T]: SinonMatcher | MatchArguments<T[K]> | T[K];
+        [K in keyof T]: SinonMatcher
+            | (T[K] extends object ? MatchArguments<T[K]> : never)
+            | T[K];
     };
 
     interface SinonSpyCallApi<TArgs extends any[] = any[], TReturnValue = any> {
@@ -29,7 +31,7 @@ declare namespace Sinon {
          * so a call that received the provided arguments (in the same spots) and possibly others as well will return true.
          * @param args
          */
-        calledWith(...args: MatchArguments<TArgs>): boolean;
+        calledWith(...args: Partial<MatchArguments<TArgs>>): boolean;
         /**
          * Returns true if spy was called at least once with the provided arguments and no others.
          */
@@ -136,41 +138,17 @@ declare namespace Sinon {
         /**
          * Returns true if the spy call occurred before another spy call.
          * @param call
+         *
          */
-        calledBefore(call: SinonSpyCall): boolean;
+        calledBefore(call: SinonSpyCall<any>): boolean;
         /**
          * Returns true if the spy call occurred after another spy call.
          * @param call
          */
-        calledAfter(call: SinonSpyCall): boolean;
-    }
-
-    /**
-     * A test spy is a function that records arguments, return value,
-     * the value of this and exception thrown (if any) for all its calls.
-     */
-    interface SinonSpy<TArgs extends any[] = any[], TReturnValue = any> extends SinonInspectable<TArgs, TReturnValue> {
-        // Methods
-        (...args: TArgs): TReturnValue;
-
-        /**
-         * Creates a spy that only records calls when the received arguments match those passed to withArgs.
-         * This is useful to be more expressive in your assertions, where you can access the spy with the same call.
-         * @param args Expected args
-         */
-        withArgs(...args: MatchArguments<TArgs>): SinonSpy<TArgs, TReturnValue>;
-
-        /**
-         * Set the displayName of the spy or stub.
-         * @param name
-         */
-        named(name: string): SinonSpy<TArgs, TReturnValue>;
+        calledAfter(call: SinonSpyCall<any>): boolean;
     }
 
-    /**
-     * The part of the spy API that allows inspecting the calls made on a spy.
-     */
-    interface SinonInspectable<TArgs extends any[] = any[], TReturnValue = any>
+    interface SinonSpy<TArgs extends any[] = any[], TReturnValue = any>
         extends Pick<
                 SinonSpyCallApi<TArgs, TReturnValue>,
                 Exclude<keyof SinonSpyCallApi<TArgs, TReturnValue>, 'args'>
@@ -234,26 +212,37 @@ declare namespace Sinon {
          * If the call did not explicitly return a value, the value at the call’s location in .returnValues will be undefined.
          */
         returnValues: TReturnValue[];
+
+        // Methods
+        (...args: TArgs): TReturnValue;
+
         /**
          * Returns true if the spy was called before @param anotherSpy
          * @param anotherSpy
          */
-        calledBefore(anotherSpy: SinonInspectable): boolean;
+        calledBefore(anotherSpy: SinonSpy<any>): boolean;
         /**
          * Returns true if the spy was called after @param anotherSpy
          * @param anotherSpy
          */
-        calledAfter(anotherSpy: SinonInspectable): boolean;
+        calledAfter(anotherSpy: SinonSpy<any>): boolean;
         /**
          * Returns true if spy was called before @param anotherSpy, and no spy calls occurred between spy and @param anotherSpy.
          * @param anotherSpy
          */
-        calledImmediatelyBefore(anotherSpy: SinonInspectable): boolean;
+        calledImmediatelyBefore(anotherSpy: SinonSpy<any>): boolean;
         /**
          * Returns true if spy was called after @param anotherSpy, and no spy calls occurred between @param anotherSpy and spy.
          * @param anotherSpy
          */
-        calledImmediatelyAfter(anotherSpy: SinonInspectable): boolean;
+        calledImmediatelyAfter(anotherSpy: SinonSpy<any>): boolean;
+
+        /**
+         * Creates a spy that only records calls when the received arguments match those passed to withArgs.
+         * This is useful to be more expressive in your assertions, where you can access the spy with the same call.
+         * @param args Expected args
+         */
+        withArgs(...args: MatchArguments<TArgs>): SinonSpy<TArgs, TReturnValue>;
         /**
          * Returns true if the spy was always called with @param obj as this.
          * @param obj
@@ -308,6 +297,11 @@ declare namespace Sinon {
          * Returns an Array with all callbacks return values in the order they were called, if no error is thrown.
          */
         invokeCallback(...args: TArgs): void;
+        /**
+         * Set the displayName of the spy or stub.
+         * @param name
+         */
+        named(name: string): SinonSpy<TArgs, TReturnValue>;
         /**
          * Returns the nth call.
          * Accessing individual calls helps with more detailed behavior verification when the spy is called more than once.
@@ -637,12 +631,14 @@ declare namespace Sinon {
     }
 
     interface SinonStubStatic {
-        // Disable rule so assignment to typed stub works (see examples in tests).
+        /* tslint:disable:no-unnecessary-generics */
+
         /**
          * Creates an anonymous stub function
          */
-        // tslint:disable-next-line no-unnecessary-generics
-        <TArgs extends any[]= any[], R = any>(): SinonStub<TArgs, R>;
+        <TArgs extends any[] = any[], R = any>(): SinonStub<TArgs, R>;
+
+        /* tslint:enable:no-unnecessary-generics */
 
         /**
          * Stubs all the object’s methods.
@@ -1162,64 +1158,66 @@ declare namespace Sinon {
         pass(assertion: any): void; // Overridable
 
         // Methods
+
         /**
          * Passes if spy was never called
          * @param spy
          */
-        notCalled(spy: SinonInspectable): void;
+        notCalled(spy: SinonSpy<any>): void;
         /**
          * Passes if spy was called at least once.
          */
-        called(spy: SinonInspectable): void;
+        called(spy: SinonSpy<any>): void;
         /**
          * Passes if spy was called once and only once.
          */
-        calledOnce(spy: SinonInspectable): void;
+        calledOnce(spy: SinonSpy<any>): void;
         /**
          * Passes if spy was called exactly twice.
          */
-        calledTwice(spy: SinonInspectable): void;
+        calledTwice(spy: SinonSpy<any>): void;
         /**
          * Passes if spy was called exactly three times.
          */
-        calledThrice(spy: SinonInspectable): void;
+        calledThrice(spy: SinonSpy<any>): void;
         /**
          * Passes if spy was called exactly num times.
          */
-        callCount(spy: SinonInspectable, count: number): void;
+        callCount(spy: SinonSpy<any>, count: number): void;
         /**
          * Passes if provided spies were called in the specified order.
          * @param spies
          */
-        callOrder(...spies: SinonInspectable[]): void;
+        callOrder(...spies: Array<SinonSpy<any>>): void;
         /**
          * Passes if spy was ever called with obj as its this value.
          * It’s possible to assert on a dedicated spy call: sinon.assert.calledOn(spy.firstCall, arg1, arg2, ...);.
          */
-        calledOn(spyOrSpyCall: SinonInspectable | SinonSpyCall, obj: any): void;
+        calledOn(spyOrSpyCall: SinonSpy<any> | SinonSpyCall<any>, obj: any): void;
         /**
          * Passes if spy was always called with obj as its this value.
          */
-        alwaysCalledOn(spy: SinonInspectable, obj: any): void;
+        alwaysCalledOn(spy: SinonSpy<any>, obj: any): void;
+
         /**
          * Passes if spy was called with the provided arguments.
          * It’s possible to assert on a dedicated spy call: sinon.assert.calledWith(spy.firstCall, arg1, arg2, ...);.
          * @param spyOrSpyCall
          * @param args
          */
-        calledWith<TArgs extends any[]>(spyOrSpyCall: SinonInspectable<TArgs> | SinonSpyCall<TArgs>, ...args: MatchArguments<TArgs>): void;
+        calledWith<TArgs extends any[]>(spyOrSpyCall: SinonSpy<TArgs> | SinonSpyCall<TArgs>, ...args: MatchArguments<TArgs>): void;
         /**
          * Passes if spy was always called with the provided arguments.
          * @param spy
          * @param args
          */
-        alwaysCalledWith<TArgs extends any[]>(spy: SinonInspectable<TArgs>, ...args: MatchArguments<TArgs>): void;
+        alwaysCalledWith<TArgs extends any[]>(spy: SinonSpy<TArgs>, ...args: MatchArguments<TArgs>): void;
         /**
          * Passes if spy was never called with the provided arguments.
          * @param spy
          * @param args
          */
-        neverCalledWith<TArgs extends any[]>(spy: SinonInspectable<TArgs>, ...args: MatchArguments<TArgs>): void;
+        neverCalledWith<TArgs extends any[]>(spy: SinonSpy<TArgs>, ...args: MatchArguments<TArgs>): void;
         /**
          * Passes if spy was called with the provided arguments and no others.
          * It’s possible to assert on a dedicated spy call: sinon.assert.calledWithExactly(spy.getCall(1), arg1, arg2, ...);.
@@ -1227,68 +1225,70 @@ declare namespace Sinon {
          * @param args
          */
         calledWithExactly<TArgs extends any[]>(
-            spyOrSpyCall: SinonInspectable<TArgs> | SinonSpyCall<TArgs>,
+            spyOrSpyCall: SinonSpy<TArgs> | SinonSpyCall<TArgs>,
             ...args: MatchArguments<TArgs>
         ): void;
         /**
          * Passes if spy was always called with the provided arguments and no others.
          */
-        alwaysCalledWithExactly<TArgs extends any[]>(spy: SinonInspectable<TArgs>, ...args: MatchArguments<TArgs>): void;
+        alwaysCalledWithExactly<TArgs extends any[]>(spy: SinonSpy<TArgs>, ...args: MatchArguments<TArgs>): void;
         /**
          * Passes if spy was called with matching arguments.
          * This behaves the same way as sinon.assert.calledWith(spy, sinon.match(arg1), sinon.match(arg2), ...).
          * It’s possible to assert on a dedicated spy call: sinon.assert.calledWithMatch(spy.secondCall, arg1, arg2, ...);.
          */
         calledWithMatch<TArgs extends any[]>(
-            spyOrSpyCall: SinonInspectable<TArgs> | SinonSpyCall<TArgs>,
+            spyOrSpyCall: SinonSpy<TArgs> | SinonSpyCall<TArgs>,
             ...args: TArgs
         ): void;
         /**
          * Passes if spy was always called with matching arguments.
          * This behaves the same way as sinon.assert.alwaysCalledWith(spy, sinon.match(arg1), sinon.match(arg2), ...).
          */
-        alwaysCalledWithMatch<TArgs extends any[]>(spy: SinonInspectable<TArgs>, ...args: TArgs): void;
+        alwaysCalledWithMatch<TArgs extends any[]>(spy: SinonSpy<TArgs>, ...args: TArgs): void;
         /**
          * Passes if spy was never called with matching arguments.
          * This behaves the same way as sinon.assert.neverCalledWith(spy, sinon.match(arg1), sinon.match(arg2), ...).
          * @param spy
          * @param args
          */
-        neverCalledWithMatch<TArgs extends any[]>(spy: SinonInspectable<TArgs>, ...args: TArgs): void;
+        neverCalledWithMatch<TArgs extends any[]>(spy: SinonSpy<TArgs>, ...args: TArgs): void;
         /**
          * Passes if spy was called with the new operator.
          * It’s possible to assert on a dedicated spy call: sinon.assert.calledWithNew(spy.secondCall, arg1, arg2, ...);.
          * @param spyOrSpyCall
          */
-        calledWithNew(spyOrSpyCall: SinonInspectable | SinonSpyCall): void;
+        calledWithNew(spyOrSpyCall: SinonSpy<any> | SinonSpyCall<any>): void;
         /**
          * Passes if spy threw any exception.
          */
-        threw(spyOrSpyCall: SinonInspectable | SinonSpyCall): void;
+        threw(spyOrSpyCall: SinonSpy<any> | SinonSpyCall<any>): void;
         /**
          * Passes if spy threw the given exception.
          * The exception is an actual object.
          * It’s possible to assert on a dedicated spy call: sinon.assert.threw(spy.thirdCall, exception);.
          */
-        threw(spyOrSpyCall: SinonInspectable | SinonSpyCall, exception: string): void;
+        threw(spyOrSpyCall: SinonSpy<any> | SinonSpyCall<any>, exception: string): void;
         /**
          * Passes if spy threw the given exception.
          * The exception is a String denoting its type.
          * It’s possible to assert on a dedicated spy call: sinon.assert.threw(spy.thirdCall, exception);.
          */
-        threw(spyOrSpyCall: SinonInspectable | SinonSpyCall, exception: any): void;
+        threw(spyOrSpyCall: SinonSpy<any> | SinonSpyCall<any>, exception: any): void;
+
         /**
          * Like threw, only required for all calls to the spy.
          */
-        alwaysThrew(spy: SinonInspectable): void;
+        alwaysThrew(spy: SinonSpy<any>): void;
         /**
          * Like threw, only required for all calls to the spy.
          */
-        alwaysThrew(spy: SinonInspectable, exception: string): void;
+        alwaysThrew(spy: SinonSpy<any>, exception: string): void;
         /**
          * Like threw, only required for all calls to the spy.
          */
-        alwaysThrew(spy: SinonInspectable, exception: any): void;
+        alwaysThrew(spy: SinonSpy<any>, exception: any): void;
+
         /**
          * Uses sinon.match to test if the arguments can be considered a match.
          */
diff --git a/types/sinon/ts3.1/sinon-tests.ts b/types/sinon/ts3.1/sinon-tests.ts
index 05b582b9db0e6a..c7bd7a6c9c4dae 100644
--- a/types/sinon/ts3.1/sinon-tests.ts
+++ b/types/sinon/ts3.1/sinon-tests.ts
@@ -82,6 +82,7 @@ function testSandbox() {
     const stubInstance = sb.createStubInstance(cls);
     const privateFooStubbedInstance = sb.createStubInstance(PrivateFoo);
     stubInstance.foo.calledWith('foo', 1);
+    stubInstance.foo.calledWith('foo');
     privateFooStubbedInstance.foo.calledWith();
     const clsFoo: sinon.SinonStub<[string, number], number> = stubInstance.foo;
     const privateFooFoo: sinon.SinonStub<[], void> = privateFooStubbedInstance.foo;