Past theoretical intersymbol interference studies aimed at finding optimal overall network characteristics have not given much attention to design limitations. In this paper we address the problem of identifying, from an ensemble of filters, that optimal filter design which maximizes a sampling signal to intersymbol interference noise power ratio. Sufficient conditions are given for such non-linear extremal problems to be well posed. Continuing under mild assumptions, attention is then focused on networks of parallel structure. In this case a procedure for constructing a solution is given. The parallel structure solution provides a partial solution to more complex network design problems. Examples of R–C and bandlimited network ensembles are considered in detail. Finally it is shown that these non-linear extremal problems generally lie outside the realm of more standard frequency domain norm minimization problems such as weighted least squares and minimax. The development is general enough to encompass design parameters having components in function space.