def discard_scores(numlist):
    """Filter numlist: construct a new list from numlist with
    the first two, and then the lowest two, scores discarded.
    """
    newlist = numlist[2:]
    least = [-1,-1]
    for i in range(len(newlist)):
        if least[0] == -1 or newlist[i] < least[0]:
            least[1] = least[0]
            least[0] = newlist[i]
        elif least[1] == -1 or newlist[i] < least[1]:
            least[1] = newlist[i]
    newlist.remove(least[0])
    newlist.remove(least[1])
    return newlist