We suggest a wavelet filtering technique as a remedy to the problem of measurement errors when testing for cointegration using Johansen’s (1988) likelihood ratio test. Measurement errors, which more or less are always present in empirical economic data, essentially indicates that the variable of interest (the true signal) is contaminated with noise, which may induce biased and inconsistent estimates and erroneous inference. Our Monte Carlo experiments demonstrate that measurement errors distort the statistical size of Johansen’s cointegration test in finite samples; the test is significantly oversized. A contribution and major finding of this article is that the proposed wavelet-based technique significantly improves the statistical size of the traditional Johansen test in small and medium sized samples. Since Johansen’s test is a standard cointegration test, and we demonstrate that the constantly present measurement errors in empirical data over sizes the test, this simple alteration can be used in most situations with more reliable finite sample inference. We empirically examine the long-run relation between CO2 emissions and the real GDP in the G7 countries. The traditional Johansen tests provide evidence of an equilibrium relation for Canada and weak evidence for the US. However, the suggested size-unbiased wavelet-filtering approach consistently indicates no evidence of cointegration for all six countries.