The size of the confidence bands for linear regression functions proposed in the literature is random. In this paper we construct confidence bands, whose size (width, content etc.) over a certain range for the regressor does not exceed a given value. We solve this problem by generalization of the known STEIN idea of two-stage confidence intervals. We propose two different two-stage procedures. The first procedure is based on an F-distribution and the margins of the bands are “surfaces of second order”. The second procedure is based on a multidimensional t-distribution and the margins are “hyperplanes”. We explain connections with problems of optimal design and with applications of linear and nonlinear programming considering estimated coefficients.