Transmission bottlenecks limit the spread of novel mutations and reduce the efficiency of selection along a transmission chain. While increased force of infection, receptor binding, or immune evasion may influence bottleneck size, the relationship between transmissibility and the transmission bottleneck is unclear. Here we compare the transmission bottleneck of non-VOC SARS-CoV-2 lineages to those of Alpha, Delta, and Omicron. We sequenced viruses from 168 individuals in 65 households. Most virus populations had 0–1 single nucleotide variants (iSNV). From 64 transmission pairs with detectable iSNV, we identify a per clade bottleneck of 1 (95% CI 1–1) for Alpha, Delta, and Omicron and 2 (95% CI 2–2) for non-VOC. These tight bottlenecks reflect the low diversity at the time of transmission, which may be more pronounced in rapidly transmissible variants. Tight bottlenecks will limit the development of highly mutated VOC in transmission chains, adding to the evidence that selection over prolonged infections may drive their evolution.