We consider, for an integer time series, two families of constraints restricting the max, and the sum, respectively, of the surfaces of the elements of the sub-series corresponding to occurrences of some pattern. In recent work these families were identified as the most difficult to solve compared to all other time-series constraints. For all patterns of the time-series constraints catalogue, we provide a unique per family parameterised among implied constraint that can be imposed on any prefix/suffix of a time-series. Experiments show that it reduces both the number of backtracks/time spent by up to 4/3 orders of magnitude.