Surprised you didn't have `sum(map(int, number_string))` in there.

  In [5]: def f(x):
     ...:     x = str(x)
     ...:     return sum(map(int, x))

  In [6]: %timeit second_way_optimized(x)
  1000 loops, best of 3: 200 µs per loop

  In [7]: %timeit f(x)
  1000 loops, best of 3: 223 µs per loop

Marginally slower, a hell of a lot easier to read what's going on.