P-ideal dichotomy and a strong form of the Suslin Hypothesis

We introduce a forcing notion which forces the P-ideal dichotomy, while every almost Suslin tree from the ground model remains non-special. Thus, while the P-ideal dichotomy implies the Suslin Hypothesis, or equivalently that every Aronszajn tree has an uncountable antichain, it does not imply that every Aronszajn tree has a stationary antichain.