We answer the long-standing question whether it is consistent to have simple $P$-points of two different characters. For a filter $\mathcal F$ over $\omega$ Guzm\'{a}n and Kalajdzievski introduced a parametrised version of Miller forcing called ${\mathbb{PT}}(\mathcal F)$. By combining iterands of the type ${\mathbb{PT}}(\mathcal F)$ with another parametrised type of iterand we establish:It is consistent relative to ZFC that there is a simple $P_{\aleph_1}$-point and a simple $P_{\aleph_2}$-point. A main technical point is the use of properness and descriptive complexity in the limit steps of uncountable cofinality. This is joint work with Christian Br\"auninger.