Abstract Polarization of radio pulsar profiles involves a number of poorly understood, intriguing phenomena, such as the existence of comparable amounts of orthogonal polarization modes (OPMs), strong distortions of polarization angle (PA) curves into shapes inconsistent with the rotating vector model (RVM), and the strong circular polarization V which can be maximum (instead of zero) at the OPM jumps. It is shown that the comparable OPMs and large V result from a coherent addition of phase-delayed waves in natural propagation modes, which are produced by a linearly polarized emitted signal. The coherent mode summation implies opposite polarization properties to those known from the incoherent case, in particular, the OPM jumps occur at peaks of V, whereas V changes sign at a maximum linear polarization fraction L/I. These features are indispensable to interpret various observed polarization effects. It is shown that statistical properties of emission and propagation can be efficiently parametrized in a simple model of coherent mode addition, which is successfully applied to complex polarization phenomena, such as the stepwise PA curve of PSR B1913+16 and the strong PA distortions within core components of pulsars B1933+16 and B1237+25. The inclusion of coherent mode addition opens the possibility for a number of new polarization effects, such as inversion of relative modal strength, twin minima in L/I coincident with peaks in V, 45° PA jumps in weakly polarized emission, and loop-shaped core PA distortions. The empirical treatment of the coherency of mode addition makes it possible to advance the understanding of pulsar polarization beyond the RVM model.