Higher security and lower failure probability have always been people's pursuits in quantum-oblivious-key-transfer-based private query (QOKT-PQ) protocols since Jacobi et al. [Phys. Rev. A 83, 022301 (2011)] proposed the first protocol of this kind. However, higher database security generally has to be obtained at the cost of a higher failure probability, and vice versa. Recently, based on a round-robin differential-phase-shift quantum key distribution protocol, Liu et al. [Sci. China-Phys. Mech. Astron., 58, 100301 (2015)] presented a private query protocol (RRDPS-PQ protocol) utilizing ideal single-photon signal which realizes both ideal database security and zero failure probability. However, ideal single-photon source is not available today, and for large database the required pulse train is too long to implement. Here, we reexamine the security of RRDPS-PQ protocol under imperfect source and present an improved protocol using a special “low-shift and addition” (LSA) technique, which not only can be used to query from large database but also retains the features of “ideal database security” and “zero-failure” even under weak coherent source. Finally, we generalize the LSA technique and establish a generic QOKT-PQ model in which both “ideal database security” and “zero failure” are achieved via acceptable communications.