This paper provides a number of working tools for the discussion of fully nonlinear parabolic equations. These include: a full proof that the maximum principle which provides \(L^\infty\) estimates of “strong” solutions of extremal equations by \(L^{n+1}\) norms of the forcing term over the “contact set” ramains valid for viscosity solutions in an \(L^{n+1}\) sense, and merely measurable forcing, a gradient estimate in \(L^p\) for \(p<(n+1)(n+2)\) for solutions of extremal equations with forcing terms in \(L^{n+1}\), the use of this estimate in improving the range of \(p\) for which the maximum principle first alluded to holds (obtaining some \(p<n+1\) – but without the contact set), a proof of the strong solvability of Dirichlet problems for extremal equations with forcing terms in \(L^p\) for some \(p<n+1\), and the twice parabolic differentiability a.e. of \(W^{2,1,p}\) functions for \((n+2)/2<p\).