The paper addresses the problem of obtaining consistent dynamic models for certain ill-conditioned plants like distillation columns. Due to strong interactions there is often a single dominating slow mode (pole) that results in similar first-order responses for all outputs. Typically, models are identified on the basis of fitting individual responses, but unless special care is taken this will result in an inconsistent overall model with the slow pole repeated. It is shown that such models with excessive slow poles, although a reasonable approximation for open-loop dynamics, yield a poor prediction of the closed-loop behavior of the process, in particular under partial control.