This paper considers the problems of local asymptotic stabilization using continuous static state feedback (LCFS) and small time local controllability (STLC) of single-input nonlinear systems. A specific class of nontriangular systems, called the essentially triangular form (ETF), is introduced. For this class of systems sufficient conditions for LCFS and necessary and sufficient conditions for STLC are obtained. In particular, it is shown that STLC implies LCFS. A motivating physical example of the ETF system is presented.