We present two gradient flow evolutions, both obtained with alternate schemes for separately-quadratic phase-field energies. The first, in the plane strain setting, features a monotonicity constraint (in time) and a multi-step scheme, for better numerical results. The second, in higher dimension, features instead a penalty method. In this case, strong compactness of the phase-field variable allows to characterize evolutions in terms of curves of maximal slope with respect to the penalty-metric.