Hirsch's h index is becoming the standard measure of an individual's research accomplishments. The aggregation of individuals' measures is also the basis for global measures at institutional or national levels. To investigate whether the h index can be reliably computed through alternative sources of citation records, the Web of Science (WoS), PsycINFO and Google Scholar (GS) were used to collect citation records for known publications of four Spanish psychologists. Compared with WoS, PsycINFO included a larger percentage of publication records, whereas GS outperformed WoS and PsycINFO in this respect. Compared with WoS, PsycINFO retrieved a larger number of citations in unique areas of psychology, but it retrieved a smaller number of citations in areas that are close to statistics or the neurosciences, whereas GS retrieved the largest numbers of citations in all cases. Incorrect citations were scarce in Wos (0.3%), more prevalent in PsycINFO (1.1%), and overwhelming in GS (16.5%). All platforms retrieved unique citations, the largest set coming from GS. WoS and PsycINFO cover distinct areas of psychology unevenly, thus applying different penalties on the h index of researches working in different fields. Obtaining fair and accurate h indices required the union of citations retrieved by all three platforms.