diff --git a/waflib/Runner.py b/waflib/Runner.py
index 70b804df..b171ed42 100644
--- a/waflib/Runner.py
+++ b/waflib/Runner.py
@@ -6,7 +6,7 @@
 Runner.py: Task scheduling and execution
 """
 
-import random
+import heapq
 try:
 	from queue import Queue
 except ImportError:
@@ -18,6 +18,31 @@ GAP = 20
 Wait for at least ``GAP * njobs`` before trying to enqueue more tasks to run
 """
 
+class PriorityTasks(object):
+	def __init__(self):
+		self.lst = []
+	def __len__(self):
+		return len(self.lst)
+	def __iter__(self):
+		return iter(self.lst)
+	def clear(self):
+		self.lst = []
+	def append(self, task):
+		heapq.heappush(self.lst, task)
+	def pop(self):
+		return heapq.heappop(self.lst)
+	def extend(self, lst):
+		if self.lst:
+			# TODO no heapq.merge in Python 2.5
+			for x in lst:
+				self.append(x)
+		else:
+			if isinstance(lst, list):
+				self.lst = lst
+				heapq.heapify(lst)
+			else:
+				self.lst = lst.queue
+
 class Consumer(Utils.threading.Thread):
 	"""
 	Daemon thread object that executes a task. It shares a semaphore with
@@ -102,11 +127,11 @@ class Parallel(object):
 		Instance of :py:class:`waflib.Build.BuildContext`
 		"""
 
-		self.outstanding = Utils.deque()
-		"""List of :py:class:`waflib.Task.Task` that may be ready to be executed"""
+		self.outstanding = PriorityTasks()
+		"""Heap of :py:class:`waflib.Task.Task` that may be ready to be executed"""
 
-		self.postponed = Utils.deque()
-		"""List of :py:class:`waflib.Task.Task` which are not ready to run for non-DAG reasons"""
+		self.postponed = PriorityTasks()
+		"""Heap of :py:class:`waflib.Task.Task` which are not ready to run for non-DAG reasons"""
 
 		self.incomplete = set()
 		"""List of :py:class:`waflib.Task.Task` waiting for dependent tasks to complete (DAG)"""
@@ -155,7 +180,7 @@ class Parallel(object):
 		"""
 		if not self.outstanding:
 			return None
-		return self.outstanding.popleft()
+		return self.outstanding.pop()
 
 	def postpone(self, tsk):
 		"""
@@ -165,10 +190,7 @@ class Parallel(object):
 		:param tsk: task instance
 		:type tsk: :py:class:`waflib.Task.Task`
 		"""
-		if random.randint(0, 1):
-			self.postponed.appendleft(tsk)
-		else:
-			self.postponed.append(tsk)
+		self.postponed.append(tsk)
 
 	def refill_task_list(self):
 		"""
@@ -207,38 +229,24 @@ class Parallel(object):
 				# We cannot use a priority queue because the implementation
 				# must be able to handle postponed dependencies
 				self.outstanding.extend(ready)
-				self.postponed.extend(waiting)
+				self.incomplete.update(waiting)
 				self.total = self.bld.total()
 				break
 
-	def insert_with_prio(self, tsk):
-		# TODO the deque interface has insert in python 3.5 :-/
-		if self.outstanding:
-			try:
-				if tsk.prio >= self.outstanding[0].prio:
-					self.outstanding.appendleft(tsk)
-				else:
-					self.outstanding.append(tsk)
-			except AttributeError:
-				self.outstanding.appendleft(tsk)
-		else:
-			self.outstanding.append(tsk)
-
 	def add_more_tasks(self, tsk):
 		"""
 		If a task provides :py:attr:`waflib.Task.Task.more_tasks`, then the tasks contained
 		in that list are added to the current build and will be processed before the next build group.
 
-		The priorities for dependent tasks are not calculated globally
+		The priorities for dependent tasks are not re-calculated globally
 
 		:param tsk: task instance
 		:type tsk: :py:attr:`waflib.Task.Task`
 		"""
 		if getattr(tsk, 'more_tasks', None):
+			# TODO recompute priorities globally?
 			ready, waiting = self.prio_and_split(tsk.more_tasks)
-			for k in ready:
-				# TODO could be better, but we will have 1 task in general?
-				self.insert_with_prio(k)
+			self.outstanding.extend(ready)
 			self.incomplete.update(waiting)
 			self.total += len(tsk.more_tasks)
 
@@ -253,7 +261,7 @@ class Parallel(object):
 						break
 				else:
 					self.incomplete.remove(x)
-					self.insert_with_prio(x)
+					self.outstanding.append(x)
 
 		if tsk in self.revdeps:
 			for x in self.revdeps[tsk]:
@@ -468,13 +476,13 @@ class Parallel(object):
 				n.visited = 1
 				if n in reverse:
 					rev = reverse[n]
-					n.prio = n.priority() + len(rev) + sum(visit(k) for k in rev)
+					n.__order = n.priority() + len(rev) + sum(visit(k) for k in rev)
 				else:
-					n.prio = n.priority()
+					n.__order = n.priority()
 				n.visited = 2
 			elif n.visited == 1:
 				raise Errors.WafError('Dependency cycle found!')
-			return n.prio
+			return n.__order
 
 		for x in tasks:
 			if x.visited != 0:
@@ -494,8 +502,6 @@ class Parallel(object):
 					break
 			else:
 				ready.append(x)
-
-		ready.sort(key=lambda x: x.prio, reverse=True)
 		return (ready, waiting)
 
 	def debug_cycles(self, tasks, reverse):
diff --git a/waflib/Task.py b/waflib/Task.py
index 37bee4f2..3628b7dd 100644
--- a/waflib/Task.py
+++ b/waflib/Task.py
@@ -153,7 +153,7 @@ class Task(evil):
 	This may be useful for certain extensions but it can a lot of memory.
 	"""
 
-	__slots__ = ('hasrun', 'generator', 'env', 'inputs', 'outputs', 'dep_nodes', 'run_after')
+	__slots__ = ('hasrun', 'generator', 'env', 'inputs', 'outputs', 'dep_nodes', 'run_after', '__order')
 
 	def __init__(self, *k, **kw):
 		self.hasrun = NOT_RUN
@@ -177,6 +177,18 @@ class Task(evil):
 		self.run_after = set()
 		"""Set of tasks that must be executed before this one"""
 
+		self.__order = 0
+		"""Task build order; used internally"""
+
+	def __lt__(self, other):
+		return self.__order > other.__order or id(self) > id(other)
+	def __le__(self, other):
+		return self.__order >= other.__order or id(self) >= id(other)
+	def __gt__(self, other):
+		return self.__order < other.__order or id(self) < id(other)
+	def __ge__(self, other):
+		return self.__order <= other.__order or id(self) <= id(other)
+
 	def get_cwd(self):
 		"""
 		:return: current working directory
@@ -213,7 +225,7 @@ class Task(evil):
 		"""
 		The default priority for this task instance
 
-		:return: a positive numeric value representing the urgency of running this task early
+		:return: a numeric value representing the urgency of running this task (the higher, the sooner)
 		:rtype: int
 		"""
 		return getattr(self, 'weight', 0)