We present a theoretical and experimental study on increasing the sensitivity of ITP assays by varying channel cross-section. We present a simple, unsteady, diffusion-free model for plateau mode ITP in channels with axially varying cross-section. Our model takes into account detailed chemical equilibrium calculations and handles arbitrary variations in channel cross-section. We have validated our model with numerical simulations of a more comprehensive model of ITP. We show that using strongly convergent channels can lead to a large increase in sensitivity and simultaneous reduction in assay time, compared to uniform cross-section channels. We have validated our theoretical predictions with detailed experiments by varying channel geometry and analyte concentrations. We show the effectiveness of using strongly convergent channels by demonstrating indirect fluorescence detection with a sensitivity of 100 nM. We also present simple analytical relations for dependence of zone length and assay time on geometric parameters of strongly convergent channels. Our theoretical analysis and experimental validations provide useful guidelines on optimizing chip geometry for maximum sensitivity under constraints of required assay time, chip area and power supply.