The Integrated Sachs-Wolfe effect is studied in non-standard cosmologies. By considering flat universes with a non-fluctuating dark energy component, it is shown how the quadrupole power can be suppressed by atypical evolution of the scale factor. For example, a brief period of non-standard evolution at a high redshift can suppress the quadrupole significantly. The effect on the overall normalization of the CMB power spectrum is also discussed. Non-standard cosmologies can affect the overall normalization significantly and enhance the primordial fluctuations. The possibility of constraining such non-standard models with CMB and independent measures of $sigma_8$, is considered.
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