A serial-flow filtration device is provided with pressure-activated means for by-passing at least one of its constituent layer (or layers) of filtration material. The filtration device comprises a housing, a fluid inlet, a fluid outlet, and at least an upper and a rearmost filter layer. The upper filter layer divides the interior of the housing into an upstream zone and a downstream zone, with the rearmost filter layer residing in the downstream zone. The fluid inlet enables the introduction of fluid into said upstream zone. The fluid outlet enables releases of the fluid from said downstream zone. The upper filter layer, but not the rearmost filter layer, has integrated thereinto a pressure-activated means capable of allowing substantially non-selective passage of fluid from the upstream zone into the downstream zone upon the attainment of a predetermined pressure differential across said upper filter layer. The bypass means can be embodied, for example, as a pressure-breachable seal or as a pressure-activated gate.