(This results from a disscussion with R. Pare while he was in Sydney) If A is any category define T(C)=[C,A] to be the standard parametrization of A. If T is a parametrized category, say T is good if T(f) has both adjoints for all f : C -> D. The standard parametrization is good iff A is complete and cocomplete. If H denotes the homotopy category the we know it is not complete. Heller has introduced an alternative parametrization. For any small category C, we form Top^C. This has a quillen model structure which gives a class of weak equivalences. We invert these and call the result H(C). Theorem (Heller): H is a good parametrization of H. Similarly: If U is a filter on a set X, we can define N(C) for each C by N = Set^C/U (filter-power of Set^C). Theorem: N is a good parametrization of Set^X/U. Both of these, N and H are non-standard parametrizations. Are they part of a general process to make a parametrization good? One feels that for A complete and cocomplete one needn't go beyond the standard parametrization. The standard parametrization of Set^X/U is not good (Adelman–Johnstone).