In the mirror effect, there are fewer false negatives (misses) and false positives (false alarms) for rare (low-frequency) words than for common (high-frequency) words. In the spacing effect, recognition accuracy is positively related to the interval (spacing or lag) between two presentations of an item. These effects are related in that they are both manifestations of a leapfrog effect (a weaker item jumps over a stronger item). They seem to be puzzles for traditional strength theory and at least some current global-matching models. A computational strength-based model (EICL) is proposed that incorporates excitation, inhibition, and a closed-loop learning algorithm. The model consists of three nonlinear coupled stochastic difference equations, one each for excitation (x), inhibition (y), and context (z). Strength is the algebraic sum (i.e., s = x - y + z). These equations are used to form a toy lexicon that serves as a basis for the experimental manipulations. The model can simulate the mirror effect forced-choice inequalities and the spacing effect for single-item recognition, all parameters are random variables, and the same parameter values are used for both the mirror and the spacing effects. No parameter values varied with the independent variables (word frequency for the mirror effect, lag for the spacing effect), so the model, not the parameters, is doing the work.