Research in the last decade has shown that to prove lower bounds or to derandomize polynomial identity testing (PIT) for general arithmetic circuits it suffices to solve these questions for restricted circuits. In this work, we study the smallest possibly restricted class of circuits, in particular depth- 4 circuits, which would yield such results for general circuits (that is, the complexity class VP). We show that if we can design poly( s )-time hitting-sets for a O ( log s ) circuits of size s , where a = (1) is arbitrarily small and the number of variables, or arity n , is O ( log s ) , then we can derandomize blackbox PIT for general circuits in quasipolynomial time. Further, this establishes that either E \#P/poly or that VP = VNP. We call the former model \emph{tiny} diagonal depth- 4 . Note that these are merely polynomials with arity O ( log s ) and degree ( log s ) . In fact, we show that one only needs a poly( s )-time hitting-set against individual-degree a = (1) polynomials that are computable by a size- s arity- ( log s ) circuit (note: fanin may be s ). Alternatively, we claim that, to understand VP one only needs to find hitting-sets, for depth- 3 , that have a small parameterized complexity.