This article considers an alternative way to generate attenuation poles (AP) in bandpass filter (BPF) with parallel type resonators and admittance inverters. It consists in using special transmission line resonators, in which one or two antiresonant frequencies ωp1, ωp2 are placed next to the main resonant frequency ω0. These frequencies ωp1, ωp2 are the poles of the input admittance Y(jω). Four new resonators are synthesized in the article. Two resonators generate one AP, and other two resonators generate two APs located near the passband of the BPFs. If we use mixed couplings between proposed adjacent resonators in BPF, then the total number of APs will become quite large. This is because each mixed coupling adds one AP. N-order BPF without cross coupling can has (3 N – 1) APs. The increased number of APs improves the BPF selectivity, including the one-sided one. With APs, the filter can provide increased attenuation in certain frequency bands and effectively suppress unwanted signals. A microstrip second order BPF with center frequency f0 = 1 GHz and bandwidth BW = 70 MHz, which has five APs, is designed. It is compared with third order BPFs with two APs.