Long exact sequence in etale cohomology of a pair

Question

Suppose $U\subset X$ is an open subscheme in a variety $X/k$ (both assumed as nice as possible) with complement $Z$. If these were analytic spaces, then there would be an exact sequence: $$\dots \to H^i_c(U) \to H^i_c(X) \to H^i_c(Z) \to H^{i+1}(U) \to \dots.$$ Is there a corresponding exact sequence in etale cohomology? I think one would have to be more careful with twists, what's the right statement? I think it should follow from the long exact sequence for a pair?