@@ -92,8 +92,7 @@ class BaseRunner:

         self.executor = _ensure_executor(executor)

         self.goal = goal

-        self._ntasks_is_user_specified = bool(ntasks)

-        self.ntasks = ntasks or _get_ncores(self.executor)

+        self._max_tasks = ntasks

         # if we instantiate our own executor, then we are also responsible

         # for calling 'shutdown'

@@ -103,17 +102,8 @@ class BaseRunner:

         self.log = [] if log else None

         self.task = None

-    def _get_n(self, done):

-        n = len(done)

-        if not self._ntasks_is_user_specified:

-            ntasks_new = _get_ncores(self.executor)

-            dn = ntasks_new - self.ntasks

-            if dn < 0:

-                # Cores have died or stopped

-                n = 0

-            n += dn

-            self.ntasks = ntasks_new

-        return n

+    def max_tasks(self):

+        return self._max_tasks or _get_ncores(self.executor)

 class BlockingRunner(BaseRunner):

@@ -167,7 +157,6 @@ class BlockingRunner(BaseRunner):

     def _run(self):

         first_completed = concurrent.FIRST_COMPLETED

         xs = dict()

-        done = [None] * self.ntasks

         do_log = self.log is not None

         if len(done) == 0:

@@ -176,14 +165,14 @@ class BlockingRunner(BaseRunner):

         try:

             while not self.goal(self.learner):

                 # Launch tasks to replace the ones that completed

-                # on the last iteration and check if new workers

-                # have started since the last iteration

-                n = self._get_n(done)

+                # on the last iteration, making sure to fill workers

+                # that have started since the last iteration.

+                n_new_tasks = max(0, self.max_tasks() - len(xs))

                 if do_log:

-                    self.log.append(('ask', n))

+                    self.log.append(('ask', n_new_tasks))

-                points, _ = self.learner.ask(n)

+                points, _ = self.learner.ask(n_new_tasks)

                 for x in points:

                     xs[self._submit(x)] = x

@@ -373,24 +362,23 @@ class AsyncRunner(BaseRunner):

     async def _run(self):

         first_completed = asyncio.FIRST_COMPLETED

-        xs = dict()

-        done = [None] * self.ntasks

+        xs = dict()  # The points we are waiting for

         do_log = self.log is not None

-        if len(done) == 0:

+        if self.max_tasks() < 1:

             raise RuntimeError('Executor has no workers')

         try:

             while not self.goal(self.learner):

                 # Launch tasks to replace the ones that completed

-                # on the last iteration and check if new workers

-                # have started since the last iteration

-                n = self._get_n(done)

+                # on the last iteration, making sure to fill workers

+                # that have started since the last iteration.

+                n_new_tasks = max(0, self.max_tasks() - len(xs))

                 if do_log:

-                    self.log.append(('ask', n))

+                    self.log.append(('ask', n_new_tasks))

-                points, _ = self.learner.ask(n)

+                points, _ = self.learner.ask(n_new_tasks)

                 for x in points:

                     xs[self._submit(x)] = x