Hofstadter's Q-sequence remains an enigma fifty years after its introduction. Initially, the terms of the sequence increase monotonically by 0 or 1 at a time. But the 12th term exceeds the 11th by two, and monotonicity fails shortly thereafter. In this paper, we add a third term to Hofstadter's recurrence in the most natural way. We show that this new recurrence, along with a suitable initial condition that naturally generalizes Hofstadter's initial condition, generates a sequence whose terms all increase monotonically by 0 or 1 at a time. Furthermore, we give a complete description of the resulting frequency sequence, which allows the nth term of our sequence to be computed efficiently. We conclude by showing that our sequence cannot be easily generalized.