We discuss the effect of a secondary component of the superconducting order parameter on the superfluid density in the cuprates. If we assume a main dx2−y2 gap, the most stable realization of a mixed order parameter has a time-reversal breaking dx2−y2+ıdxy symmetry. In this state the nodes are removed and the temperature dependence of the superfluid density changes from the linear behavior of a pure d wave to a more rounded shape at low temperature. The latter is compatible with the behavior experimentally observed in the in-plane magnetic field penetration depth of optimally doped La2−xSrxCuO2 and YBa2Cu3O7−y.