This paper lays the foundation of an underwater acoustic channel simulation methodology that is halfway between parametric modeling and stochastic replay of at-sea measurements of channel impulse responses. The motivation behind this approach is to extend the scope of use of replay-based methods by allowing some parameterization of the channel properties while complying with some level of realism. Based on a relative entropy minimization between the original channel impulse response and the simulated one, the idea is to deliberately distort the original channel statistics in order to meet some specified constraints.