When iterative learning control (ILC) is applied to improve a system's tracking performance, the trial-invariant reference input is typically known or contained in a prescribed set of signals. To account for this knowledge, we propose a novel ILC structure that only responds to a given set of trial-invariant inputs. The controllers are called reduced-order ILCs as their order is less than the discrete-time trial length. Exploiting all knowledge available on the input signals is instrumental in facing the fundamental performance limitations in ILC: an ILC is bound to amplify trial-varying inputs and reducing this trial-varying performance degradation invokes a slower learning transient. We present a novel optimal ILC design strategy that allows for a quantitative and systematic analysis of this tradeoff. The merit of reduced-order ILCs in view of this tradeoff is demonstrated by numerical results.