Double-sampling techniques allow to double the sampling frequency of a switched capacitor ΣΔ analog-to-digital convertors without increasing the clock frequency. Unfortunately, path mismatch between the double sampling branches may cause noise folding, which could ruin the modulator's performance. The fully floating double-sampling integrator is an interesting building block to be used in such a double sampling ΣΔ modulator because its operation is tolerant to path mismatch. However, this circuit exhibits an undesired bilinear filter effect. This effectively increases the order of the modulator by one. Due to this, previously presented structures don't have enough freedom to fully control the modulator pole positions. In this paper, we introduce modified topologies for double-sampling ΣΔ modulators built with bilinear integrators. We show that these architectures provide full control of the modulator pole positions and hence can be used to implement any noise transfer function. Additionally, analytical expressions are obtained for the residual folded noise.