diff --git a/test/async/cancellable.wast b/test/async/cancellable.wast
index a24acc85..34cd446c 100644
--- a/test/async/cancellable.wast
+++ b/test/async/cancellable.wast
@@ -4,7 +4,7 @@
 ;; Component $C exports five async callback-lifted functions that block in
 ;; their initial core function (the callbacks are never invoked):
 ;;   wait-cancel: blocks on cancellable waitable-set.wait, expects TASK_CANCELLED
-;;   yield-cancel: yields with cancellable, caller cancels during yield
+;;   yield-cancel: yields with cancellable until the caller cancels
 ;;   poll-cancel-pending: blocks on non-cancellable wait, then polls with cancellable
 ;;   yield-cancel-pending: blocks on non-cancellable wait, then yields with cancellable
 ;;
@@ -40,11 +40,11 @@
 
       ;; Test 2: direct cancel delivery through cancellable thread.yield
       (func $yield-cancel (export "yield-cancel") (result i32)
-        (local $ret i32)
-        ;; yield with cancellable; suspends with cancellable=true, caller cancels
-        (local.set $ret (call $thread.yield-cancellable))
-        (if (i32.ne (i32.const 1 (; CANCELLED ;)) (local.get $ret))
-          (then unreachable))
+        ;; yield with cancellable until cancelled by the caller (a single
+        ;; yield may nondeterministically complete without suspending and
+        ;; thus without the cancellation being delivered)
+        (loop $again
+          (br_if $again (i32.eqz (call $thread.yield-cancellable))))
         (call $task.cancel)
         (i32.const 0 (; EXIT ;))
       )
diff --git a/test/async/during-sync-call-no-exclusive-resume.wast b/test/async/during-sync-call-no-exclusive-resume.wast
index c054493d..1298fe8e 100644
--- a/test/async/during-sync-call-no-exclusive-resume.wast
+++ b/test/async/during-sync-call-no-exclusive-resume.wast
@@ -21,6 +21,7 @@
 
       (global $setup-thread-index (mut i32) (i32.const 0xdead))
       (global $implicit-thread-index (mut i32) (i32.const 0xdead))
+      (global $in-sync-call (mut i32) (i32.const 0))
 
       (func $thread-start (param i32)
         (local $r i32)
@@ -38,23 +39,31 @@
         (i32.const 0 (; EXIT ;)))
 
       ;; async callback task resolves, then parks its implicit thread, ready,
-      ;; in its event loop by returning YIELD, but must never be resumed.
+      ;; in its event loop by returning YIELD. Since a YIELD may
+      ;; nondeterministically complete without suspending, 'never-cb' may be
+      ;; called (with a NONE event) while no non-async-typed call is in
+      ;; progress and parks the thread again; it must never be called during
+      ;; 'sync-block'.
       (func (export "arm") (result i32)
         (call $task.return (i32.const 1))
         (i32.const 1 (; YIELD ;)))
 
       (func (export "never-cb") (param i32 i32 i32) (result i32)
-        unreachable)
+        (if (global.get $in-sync-call)
+          (then unreachable))
+        (i32.const 1 (; YIELD ;)))
 
       ;; non-async-typed: 4 rounds of switching to $thread-start and being made ready
       ;; again by it
       (func (export "sync-block") (result i32)
         (local $r i32)
+        (global.set $in-sync-call (i32.const 1))
         (global.set $implicit-thread-index (call $thread.index))
         (loop $rounds
           (drop (call $thread.suspend-then-resume (global.get $setup-thread-index)))
           (local.set $r (i32.add (local.get $r) (i32.const 1)))
           (br_if $rounds (i32.lt_u (local.get $r) (i32.const 4))))
+        (global.set $in-sync-call (i32.const 0))
         (i32.const 42))
     )
     (core type $start-func-ty (func (param i32)))
@@ -117,17 +126,25 @@
     (import "" "task.return" (func $task.return (param i32)))
     (import "" "thread.suspend" (func $thread.suspend (result i32)))
 
+    (global $in-sync-call (mut i32) (i32.const 0))
+
     ;; async callback task resolves, then parks its implicit thread, ready,
-    ;; in its event loop by returning YIELD, but must never be resumed.
+    ;; in its event loop by returning YIELD. Since a YIELD may
+    ;; nondeterministically complete without suspending, 'never-cb' may be
+    ;; called (with a NONE event) while no non-async-typed call is in progress
+    ;; and parks the thread again; it must never be called during 'sync-block'.
     (func (export "arm") (result i32)
       (call $task.return (i32.const 1))
       (i32.const 1 (; YIELD ;)))
 
     (func (export "never-cb") (param i32 i32 i32) (result i32)
-      unreachable)
+      (if (global.get $in-sync-call)
+        (then unreachable))
+      (i32.const 1 (; YIELD ;)))
 
     ;; non-async-typed: suspend with no valid thread to switch to
     (func (export "sync-block")
+      (global.set $in-sync-call (i32.const 1))
       (drop (call $thread.suspend))
       unreachable)
   )
diff --git a/test/async/sync-barges-in.wast b/test/async/sync-barges-in.wast
index b9eb4fa5..355b6395 100644
--- a/test/async/sync-barges-in.wast
+++ b/test/async/sync-barges-in.wast
@@ -79,11 +79,20 @@
         (global.set $unblock-value (local.get $val))
       )
 
+      ;; 'yielder'/'yielder-cb' yield until 'poker' has been called (a single
+      ;; yield may nondeterministically complete without suspending, which
+      ;; would resolve the task before the caller gets to call 'poker').
+      (global $poked (mut i32) (i32.const 0))
+
       (func (export "yielder")
-        (drop (call $thread.yield))
+        (global.set $poked (i32.const 0))
+        (loop $again
+          (drop (call $thread.yield))
+          (br_if $again (i32.eqz (global.get $poked))))
         (call $task.return (global.get $unblock-value))
       )
       (func (export "yielder-cb") (result i32)
+        (global.set $poked (i32.const 0))
         (i32.const 1 (; YIELD ;))
       )
       (func (export "yielder-cb-cb") (param $event_code i32) (param $index i32) (param $payload i32) (result i32)
@@ -93,10 +102,13 @@
           (then unreachable))
         (if (i32.ne (i32.const 0) (local.get $payload))
           (then unreachable))
+        (if (i32.eqz (global.get $poked))
+          (then (return (i32.const 1 (; YIELD ;)))))
         (call $task.return (global.get $unblock-value))
         (i32.const 0 (; EXIT ;))
       )
       (func (export "poker") (param $val i32)
+        (global.set $poked (i32.const 1))
         (global.set $unblock-value (local.get $val))
       )
     )