The existence and uniqueness in the class \(W^{2,p} \cap W_0^{1,p}\) of solutions of the elliptic equation \[ \sum^n_{i,j = 1} a_{ij} (x) {\partial^2u \over \partial x_i \partial x_j} + \sum^n_{i = 1} b_i(x) {\partial u \over \partial x} + e(x)u = f, \] assuming that the coefficients \(a_{ij}\) are in the Sarason's space VMO and the lower order terms' coefficients are taken in suitable \(L^p\) spaces, are proved.