The paper considers a new class of filters with transfer functions providing equal step-response overshoots for all filter orders. This class of filters is derived using Bessel polynomials. The proposed procedure indicates also that Bessel filters are part of a wide class of polynomial filters with prescribed step-response overshoot. The example considered in the paper describes the set of filters, from second to eight order, all having the step-response overshoot equal to 5%. The paper presents the transfer functions of the filters, their frequency responses in the pass-band and stop-band, special features of these responses in the transition zone, and gives the calculated step-response transients.