The ice strength parameter P* is a key parameter in dynamic/thermodynamic sea ice models that cannot be measured directly. Stochastically perturbing P* in the Finite Element Sea Ice–Ocean Model (FESOM) of the Alfred Wegener Institute aims at investigating the effect of uncertainty pertaining to this parameterization. Three different approaches using symmetric perturbations have been applied: 1) reassignment of uncorrelated noise fields to perturb P* at every grid point, 2) a Markov chain time correlation, and 3) a Markov chain time correlation with some spatial correlation between nodes. Despite symmetric perturbations, results show an increase of Arctic sea ice volume and a decrease of Arctic sea ice area for all three approaches. In particular, the introduction of spatial correlation leads to a substantial increase in sea ice volume and mean thickness. The strongest response can be seen for multiyear ice north of the Greenland coast. An ensemble of eight perturbed simulations generates a spread in the multiyear ice comparable to the interannual variability of the model. Results cannot be reproduced by a simple constant global modification of P*.