Detecting single nucleotide polymorphisms (SNPs) between genomes is becoming a routine task with next-generation sequencing. Generally, SNP detection methods use a reference genome. As non-model organisms are increasingly investigated, the need for reference-free methods has been amplified. Most of the existing reference-free methods have fundamental limitations: they can only call SNPs between exactly two datasets, and/or they require a prohibitive amount of computational resources. The method we propose, discoSnp, detects both heterozygous and homozygous isolated SNPs from any number of read datasets, without a reference genome, and with very low memory and time footprints (billions of reads can be analyzed with a standard desktop computer). To facilitate downstream genotyping analyses, discoSnp ranks predictions and outputs quality and coverage per allele. Compared to finding isolated SNPs using a state-of-the-art assembly and mapping approach, discoSnp requires significantly less computational resources, shows similar precision/recall values, and highly ranked predictions are less likely to be false positives. An experimental validation was conducted on an arthropod species (the tick Ixodes ricinus) on which de novo sequencing was performed. Among the predicted SNPs that were tested, 96% were successfully genotyped and truly exhibited polymorphism.