diff --git a/test_regress/t/t_disable_task_by_name.v b/test_regress/t/t_disable_task_by_name.v
index d2f86c909..f4583eb72 100644
--- a/test_regress/t/t_disable_task_by_name.v
+++ b/test_regress/t/t_disable_task_by_name.v
@@ -8,6 +8,7 @@
 
 int x = 0;
 int y = 0;
+int z = 0;
 
 int self_entry = 0;
 int self_after_disable = 0;
@@ -43,6 +44,10 @@ task increment_y;
   y++;
 endtask
 
+task finish_z;
+  z++;
+endtask
+
 task self_stop;
   self_entry = 1;
   disable self_stop;
@@ -217,6 +222,10 @@ module t;
     join_none
     #10;
     if (x != 1) $stop;
+    // Re-disabling after prior disable (no active invocations) is a no-op
+    disable increment_x;
+    #1;
+    if (x != 1) $stop;
 
     // Another basic module-task disable-by-name case
     fork
@@ -226,6 +235,13 @@ module t;
     #10;
     if (y != 1) $stop;
 
+    // Disabling a task after it already finished is a no-op
+    finish_z();
+    if (z != 1) $stop;
+    disable finish_z;
+    #1;
+    if (z != 1) $stop;
+
     // Self-disable in task by name
     self_stop();
     if (self_entry != 1) $stop;