diff --git a/Cakefile b/Cakefile
index 599520f6..243b140d 100644
--- a/Cakefile
+++ b/Cakefile
@@ -425,12 +425,6 @@ runTests = (CoffeeScript) ->
     catch err
       onFail description, fn, err
 
-  global.supportsAsync = try
-      new Function('async () => {}')()
-      yes
-    catch
-      no
-
   helpers.extend global, require './test/support/helpers'
 
   # When all the tests have run, collect and print errors.
@@ -448,10 +442,18 @@ runTests = (CoffeeScript) ->
       console.log "  #{source}" if source
     return
 
-  # Run every test in the `test` folder, recording failures.
-  files = fs.readdirSync 'test'
-  unless global.supportsAsync # Except for async tests, if async isn’t supported.
-    files = files.filter (filename) -> filename isnt 'async.coffee'
+  # Run every test in the `test` folder, recording failures, except for files
+  # we’re skipping because the features to be tested are unsupported in the
+  # current Node runtime.
+  testFilesToSkip = []
+  skipUnless = (featureDetect, filenames) ->
+    unless (try new Function featureDetect)
+      testFilesToSkip = testFilesToSkip.concat filenames
+  skipUnless 'async () => {}', ['async.coffee', 'async_iterators.coffee']
+  skipUnless 'async function* generator() { yield 42; }', ['async_iterators.coffee']
+  skipUnless 'var a = 2 ** 2; a **= 3', ['exponentiation.coffee']
+  files = fs.readdirSync('test').filter (filename) ->
+    filename not in testFilesToSkip
 
   startTime = Date.now()
   for file in files when helpers.isCoffee file
diff --git a/test/async.coffee b/test/async.coffee
index be1994c5..eb72972a 100644
--- a/test/async.coffee
+++ b/test/async.coffee
@@ -1,8 +1,9 @@
 # Functions that contain the `await` keyword will compile into async functions,
 # supported by Node 7.6+, Chrome 55+, Firefox 52+, Safari 10.1+ and Edge.
-# But runtimes that don’t support the `await` keyword will throw an error,
-# even if we put `return unless global.supportsAsync` at the top of this file.
-# Therefore we need to prevent runtimes which will choke on such code from even
+# But runtimes that don’t support the `await` keyword will throw an error just
+# from parsing this file, even without executing it, even if we put
+# `return unless try new Function 'async () => {}'` at the top of this file.
+# Therefore we need to prevent runtimes which will choke on such code from
 # parsing it, which is handled in `Cakefile`.
 
 
diff --git a/test/repl.coffee b/test/repl.coffee
index 537631e1..fb79e7f1 100644
--- a/test/repl.coffee
+++ b/test/repl.coffee
@@ -124,7 +124,7 @@ testRepl "keeps running after runtime error", (input, output) ->
   eq 'undefined', output.lastWrite()
 
 testRepl "#4604: wraps an async function", (input, output) ->
-  return unless global.supportsAsync
+  return unless try new Function 'async () => {}' # Feature detect support for async functions.
   input.emitLine 'await new Promise (resolve) -> setTimeout (-> resolve 33), 10'
   setTimeout ->
     eq '33', output.lastWrite()