|Noisy Harmonic Grammar (NHG) is a framework for stochastic grammars that uses the GEN-cum-EVAL system originated in Optimality Theory. As a form of Harmonic Grammar, NHG outputs as winner the candidate with the smallest harmonic penalty (weighted sum of constraint violations). It is stochastic because at each "evaluation time," constraint weights are nudged upward or downward by a random amount, resulting in a particular probability distribution over candidates. This "classical" form of NHG can be modified in various ways, creating alternative theories. I explore these variants in a variety of simple simulations intended to reveal key differences in their behavior; maxent grammars are also included in the comparison. In conclusion I offer hints from the empirical world regarding which of these rival theories might be correct.