Rubuta ci gaba don wannan sakin layi - mamayewar Sweden na Yaren mutanen Poland-Lithuania a shekara mai zuwa ya fara Yaƙin Arewa na Biyu. Frederick William ya ba da kariya ga garuruwan Royal Prussian a cikin Yarjejeniyar Rinsk, amma dole ne ya ba da ikon mulkin soja na Sweden kuma ya janye zuwa ga Prussian duchy. Da sojojin Sweden suka bi shi zuwa babban birnin Prussia, Frederick William ya yi zaman lafiya kuma ya yi kawance da Sweden, yana ɗaukar Duchy na Prussia da Ermland (Ermeland, Warmia) a matsayin masu mulki daga Charles X Gustav na Sweden a cikin Yarjejeniyar Königsberg a watan Janairu 1656. Ƙungiyar ta tabbatar da nasara a yakin Warsaw
a watan Yuni, yana inganta martabar masu zabe a duniya. Ci gaba da matsin lamba kan Charles X Gustav ya haifar da shi ya ba da cikakken ikon mallaka a cikin Ducal Prussia da Ermland ga Frederick William ta Yarjejeniyar Labiau a watan Nuwamba don tabbatar da ci gaba da kawancen. Yarjejeniyar Radnot, wacce aka kulla a watan Disamba ta Sweden da kawayenta, ta kuma ba da babbar Poland ga Brandenburg-Prussia idan akwai nasara.