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Process-Overlap Theory (POT) suggests that measures of cognitive abilities sample from sets of independent cognitive processes. These cognitive processes can be separated into domain-general executive processes, sampled by the majority of cognitive ability measures, and domain-specific processes, sampled only by measures within a certain domain. According to POT, fluid intelligence measures are related because different tests sample similar domain-general executive cognitive processes to some extent. Re-analyzing data from a study by De Simoni & von Bastian (2018), we assessed domain-general variance from executive processing tasks measuring inhibition, shifting, and efficiency of removal from working memory, and examined their relation to a domain-general factor extracted from fluid intelligence measures. The results showed that domain-general factors reflecting general processing speed were moderately and negatively correlated with the domain-general fluid intelligence factor (r = -.17 -- -.36). However, domain-general factors isolating variance specific to inhibition, shifting, and removal showed only small and inconsistent correlations with the domain-general fluid intelligence factor (r = .02 -- -.22). These findings suggest that (1) executive processing tasks sample only few domain-general executive processes also sampled by fluid intelligence measures, and that (2) domain-general speed of processing contributes more strongly to individual differences in fluid intelligence than do domain-general executive processes.