We are primarily concerned with minimal
P
{\text {P}}
convergence spaces, where
P
{\text {P}}
is one of the following convergence space properties: Hausdorff,
T
2
,
λ
{{\text {T}}_2}, \lambda
-regular,
λ
\lambda
-Urysohn, and first countable,
λ
\lambda
an infinite cardinal number. Our conclusions usually resemble the corresponding topological results, but with some deviations ; for instance, a minimal Hausdorff convergence space is always compact, whereas a countable minimal regular convergence space need not be compact.