This paper proposes an improvement to the original constructions of exponential attractors. An exponential attractor for a continuous map on a compact invariant set \(B\) is a compact, invariant subset \(M\) of \(B\) with finite fractal dimension that contains the global attractor \(A\) which is the \(\omega\)-limit set of \(B\) and attracts all points of \(B\) at a rate which is at least exponential. The authors propose a construction that carries through, even when the invariant set on which the solution semigroup acts is not compact. Their construction requires only that the solution semigroup be \(\alpha\)-contractive and satisfy the discrete squeezing property.