diff --git a/Tests/AllTestsCommon.swift b/Tests/AllTestsCommon.swift
index 3e23fa20..72b0ffb2 100644
--- a/Tests/AllTestsCommon.swift
+++ b/Tests/AllTestsCommon.swift
@@ -111,6 +111,27 @@ class CustomExecutorTestCase: XCTestCase {
     final func assertExecutorCalled(atLeast times: Int, file: StaticString = #file, line: UInt = #line) {
         XCTAssert(_executor.submitCount.withReadLock({ $0 >= times }), "Executor was not called enough times", file: file, line: line)
     }
+
+    final func expectationThatExecutor(isCalledAtLeast times: Int) -> XCTestExpectation {
+        return expectation(for: NSPredicate(block: { (sself, _) -> Bool in
+            guard let sself = sself as? CustomExecutorTestCase else { return false }
+            return sself._executor.submitCount.withReadLock({ $0 >= times })
+        }), evaluatedWith: self)
+    }
+
+    final let queue = DispatchQueue(label: "com.bignerdranch.DeferredTests")
+
+    final func expectQueueToBeEmpty(description: String? = nil, file: StaticString = #file, line: UInt = #line) -> XCTestExpectation {
+        let expect = expectation(description: description ?? "queue is empty")
+        queue.async(flags: .barrier) {
+#if os(macOS) || os(iOS) || os(watchOS) || os(tvOS) || !swift(>=4.1)
+            expect.fulfill()
+#else
+            expect.fulfill(file, line: line)
+#endif
+        }
+        return expect
+    }
 }
 
 extension Collection {
diff --git a/Tests/TaskTests/TaskTests.swift b/Tests/TaskTests/TaskTests.swift
index ac0a0e81..ce27bf07 100755
--- a/Tests/TaskTests/TaskTests.swift
+++ b/Tests/TaskTests/TaskTests.swift
@@ -25,7 +25,10 @@ class TaskTests: CustomExecutorTestCase {
         ("testThatRecoverMapsFailures", testThatRecoverMapsFailures),
         ("testThatMapPassesThroughErrors", testThatMapPassesThroughErrors),
         ("testThatRecoverPassesThroughValues", testThatRecoverPassesThroughValues),
-        ("testThatFallbackAlsoProducesANewTask", testThatFallbackAlsoProducesANewTask)
+        ("testThatFallbackProducesANewTask", testThatFallbackProducesANewTask),
+        ("testThatFallbackUsingCustomExecutorProducesANewTask", testThatFallbackUsingCustomExecutorProducesANewTask),
+        ("testThatFallbackReturnsOriginalSuccessValue", testThatFallbackReturnsOriginalSuccessValue),
+        ("testThatFallbackUsingCustomExecutorReturnsOriginalSuccessValue", testThatFallbackUsingCustomExecutorReturnsOriginalSuccessValue)
     ]
 
     static var allTests: [(String, (TaskTests) -> () throws -> Void)] {
@@ -268,16 +271,56 @@ class TaskTests: CustomExecutorTestCase {
     }
     #endif
 
-    func testThatFallbackAlsoProducesANewTask() {
+    func testThatFallbackProducesANewTask() {
+        let task = makeAnyFailedTask().fallback(upon: queue) { _ -> Task<Int> in
+            return self.makeAnyFinishedTask()
+        }
+
+        shortWait(for: [
+            expectation(that: task, succeedsWith: 42),
+            expectQueueToBeEmpty()
+        ])
+    }
+
+    func testThatFallbackUsingCustomExecutorProducesANewTask() {
         let task = makeAnyFailedTask().fallback(upon: executor) { _ -> Task<Int> in
             return self.makeAnyFinishedTask()
         }
 
         shortWait(for: [
-            expectation(that: task, succeedsWith: 42)
+            expectation(that: task, succeedsWith: 42),
+            expectationThatExecutor(isCalledAtLeast: 1)
         ])
+    }
 
-        assertExecutorCalled(atLeast: 2)
+    func testThatFallbackReturnsOriginalSuccessValue() {
+        let (deferred, task1) = makeAnyUnfinishedTask()
+        let task2 = task1.fallback(upon: queue) { _ -> Task<Int> in
+            return self.makeAnyFinishedTask()
+        }
+
+        let expect = expectation(that: task2, succeedsWith: 99)
+        deferred.succeed(with: 99)
+
+        shortWait(for: [
+            expect,
+            expectQueueToBeEmpty()
+        ])
+    }
+
+    func testThatFallbackUsingCustomExecutorReturnsOriginalSuccessValue() {
+        let (deferred, task1) = makeAnyUnfinishedTask()
+        let task2 = task1.fallback(upon: executor) { _ -> Task<Int> in
+            return self.makeAnyFinishedTask()
+        }
+
+        let expect = expectation(that: task2, succeedsWith: 99)
+        deferred.succeed(with: 99)
+
+        shortWait(for: [
+            expect,
+            expectationThatExecutor(isCalledAtLeast: 1)
+        ])
     }
 
     func testSimpleFutureCanBeUpgradedToTask() {