  We revisit and generalize the geometric procedure of regularizing a sequence
of real numbers with respect to a so-called regularizing function. This
approach was studied by S. Mandelbrojt and becomes useful and necessary when
working with corresponding classes of ultradifferentiable functions defined via
weight sequences and analogous weighted spaces. In this note we also study
non-standard situations for the construction yielding the (log-)convex minorant
of a sequence and allow a "blow-up" for the regularizing function.
