The point and depth spectrum of a directed set are adjoined sets of regular cardinals that can be viewed as a measure of cofinal complexity. The first was studied in the 50s and 60s by Tukey, Schmidt and Isbell, and more recently Gartside-Mamatelashvili and Gilton studied certain relations between the point spectrum and PCF theory. Here we use PCF theory to study the supremum of the point spectrum and present several results regarding the point and depth spectrum of an ultrafilter. In the second part of the talk we present a Hechler-like result, producing ultrafilter base of prescribed isomorphism type. We then use these results to obtain new consistency results- answering several questions about the spectrums and in the realm of generalized cardinal characteristics.