We consider the nonlinear algebras W (sl(4), sl (3)) and W (sl(3|1), sl (3)) and find their realizations in terms of currents spanning conformal linearizing algebras. The specific structure of these algebras, allows us to construct realizations modulo null fields of the W 3 algebra that lies in the cosets W (sl(4), sl(3))/u(1) and W (sl(3|1), sl(3))/u(1). Such realizations exist for the following values of the W 3 algebra central charge: c W = −30, −40/7, −98/5, −2. The first two values are listed for the first time, whereas for the remaining values we get the new realizations in terms of an arbitrary stress tensor and u(1) × sl(2) affine currents.