Mass-radius diagram of inner super-Earths with and without cold Jupiters. Included are all planets with masses of 1–47 M_⊕ and a < 0.3 au. Top and center panels: all such planets in SE ∩ CJ and systems, respectively, with their core ice mass fractions color-coded. Bottom panel: balanced samples (N = 190) from both system classes. On average, super-Earths in cold Jupiter-hosting systems populate regions of higher bulk density. In all panels, we overplot observed super-Earths in exoplanet systems containing both planet types, (SE ∩ CJ)_obs. These planets match their synthetic counterparts well, but fail to match the population.