Clark and the author [2] recently obtained a generalization of the Hartman-Wintner comparison theorem [4] for a pair of self-adjoint second order linear elliptic differential equations. The purpose of this note is to extend this generalization to general second order linear elliptic equations. As in [2], the usual pointwise inequalities for the coefficients are replaced by a more general integral inequality. The result is new even in the one-dimensional case, and extends Leighton's result for self-adjoint ordinary equations [5]. Protter [6] obtained pointwise inequalities in the nonself-adjoint case in two dimensions by the method of Hartman and Wintner [4]. We obtain an alternative to Protter's result as a corollary of our main theorem. Let R be a bounded domain in n-dimensional Euclidean space with boundary B having a piecewise continuous unit normal. The linear elliptic differential operator L defined by