Whole-genome amplification by multiple displacement amplification (MDA) is a promising technique to enable the use of samples with only limited amount of DNA for the construction of RAD-seq libraries. Previous work has shown that, when the amount of DNA used in the MDA reaction is large, double-digest RAD-seq (ddRAD) libraries prepared with amplified genomic DNA result in data that are indistinguishable from libraries prepared directly from genomic DNA. Based on this observation, here we evaluate the quality of ddRAD libraries prepared from MDA-amplified genomic DNA when the amount of input genomic DNA and the coverage obtained for samples is variable. By simultaneously preparing libraries for five species of weevils (Coleoptera, Curculionidae), we also evaluate the likelihood that potential contaminants will be encountered in the assembled dataset. Overall, our results indicate that MDA may not be able to rescue all samples with small amounts of DNA, but it does produce ddRAD libraries adequate for studies of phylogeography and population genetics even when conditions are not optimal. We find that MDA makes it harder to predict the number of loci that will be obtained for a given sequencing effort, with some samples behaving like traditional libraries and others yielding fewer loci than expected. This seems to be caused both by stochastic and deterministic effects during amplification. Further, the reduction in loci is stronger in libraries with lower amounts of template DNA for the MDA reaction. Even though a few samples exhibit substantial levels of contamination in raw reads, the effect is very small in the final dataset, suggesting that filters imposed during dataset assembly are important in removing contamination. Importantly, samples with strong signs of contamination and biases in heterozygosity were also those with fewer loci shared in the final dataset, suggesting that stringent filtering of samples with significant amounts of missing data is important when assembling data derived from MDA-amplified genomic DNA. Overall, we find that the combination of MDA and ddRAD results in high-quality datasets for population genetics as long as the sequence data is properly filtered during assembly.