We present Fuk-Nagaev - type inequality for the sums of independent self-adjoint operators. This bound could be viewed as an extension of the well known “Matrix Bernstein” inequality to the case of operators with heavy-tailed norms. As a corollary, we deduce Rosenthal moment inequality that improves upon the previously known versions even in the scalar case. Finally, we will discuss applications of these bounds to the covariance estimation problem.