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Suppose that φ is an analytic self-map of the unit disk Δ. We consider compactness of the composition operator C _φ from the Bloch space ℬ into the spaces Q _K defined by a nonnegative, nondecreasing function K(r) for 0 ≤ r < ∞. Our compactness condition depends only on ϕ which can be considered as a slight improvement of the known results. The compactness of C _ϕ from the Dirichlet space $${\fancyscript D}$$ into the spaces Q _K is also investigated.