Having the deque with the advantages of Queue in a thread

I need a structure where I will be able to pop() and append() to the right side (just like deque), while having the structure blocking and waiting if it is empty (just like Queue). I could directly use a Queue, but I need also the nice feature of deque where items are removed without blocking if the structure is full.

from collections import deque
d = deque(maxlen=2)
d.append(1)
d.append(2)
d.append(3) # d should be [2,3] (it is the case)
d.pop()
d.pop()
d.pop() # should wait (not the case)

Is it better to subclass deque (making it wait) or Queue (adding a popLeft function)?

What about creating your own queue mixing the best of both?

import queue as Queue
from collections import deque

class QueuePro:
  def __init__(self, maxlenDeque): 
    self.deque = deque(maxlen=maxlenDeque)
    self.queue = Queue.Queue()

  def append(self, elem):
    self.deque.append(elem)
    self.queue.put(elem)

  def pop(self):
    if(not self.deque):
      self.queue.get()
    else:
      self.deque.pop()
      self.queue.get()


q2 = QueuePro(2)
q2.append(1)
q2.append(2)

q2.pop()
q2.pop()
q2.pop()
#waiting