Derandomization of blackbox identity testing reduces to extremely special circuit models. After a line of work, it is known that focusing on circuits with constant-depth and constantly many variables is enough (Agrawal,Ghosh,Saxena, STOC'18) to get to general hitting-sets and circuit lower bounds. This inspires us to study circuits with few variables, eg.~logarithm in the size s . We give the first poly( s )-time blackbox identity test for n = O ( log s ) variate size- s circuits that have poly( s )-dimensional partial derivative space; eg.~depth- 3 diagonal circuits (or n ). The former model is well-studied (Nisan,Wigderson, FOCS'95) but no poly ( s 2 n ) -time identity test was known before us. We introduce the concept of {\em cone-closed} basis isolation and prove its usefulness in studying log-variate circuits. It subsumes the previous notions of rank-concentration studied extensively in the context of ROABP models.