A passive quantum key distribution (QKD) transmitter generates the quantum states prescribed by a QKD protocol at random, combining a fixed quantum mechanism and a post-selection step. By circumventing the use of active optical modulators externally driven by random number generators, passive QKD transmitters offer immunity to modulator side channels and potentially enable higher frequencies of operation. Recently, the first linear optics setup suitable for passive decoy-state QKD has been proposed. In this work, we simplify the prototype and adopt sharply different approaches for BB84 polarization encoding and decoy-state parameter estimation. In particular, our scheme avoids a probabilistic post-selection step that is central to the former proposal. On top of it, we elaborate a simple and tight custom-made security analysis.