This paper seeks to examine whether there is heterogeneity in the impacts of research grant funding, by examining whether before--after differences in citation impact are related to the past performance of grantees. Analysis of the heterogeneity in funding impacts can potentially inform the selection of awardees and the design of funding instruments and application and assessment procedures. We examine the impacts of research project grants awarded over the period from 2005 to 2008 from the Danish Council for Independent Research. For the matched sample of grantees and rejected applicants, mean before--after differences are significantly greater for grantees than rejected applicants. However, results are more mixed when comparing overall distributions instead of mean values, where results are either not significant or weakly significant at the 10% level. This suggests that grants lead to strong results for some but are much less for the majority of grantees. The analysis finds indications that citation impact of research grants is positively related to past research performance, thus providing indications of heterogeneity in grant effects. Additional work could be very useful in further exploring possible systematic relationships between other applicant characteristics, such as years of experience as a researcher and overall publication activity, and subsequent impacts.