In this paper we introduce and design sparse constellations for Direct-to-Satellite Internet of Things (DtS-IoT). DtS-IoT does not require a ground infrastructure, because the devices are directly connected to Low Earth Orbit satellites acting as orbiting gateways. The key idea of sparse constellations is to significantly reduce the number of in-orbit DtS-IoT satellites by (i) a proper dimensioning of the delivery delay anyway present in resource-constrained IoT services, and (ii) an optimal positioning of the orbiting gateways. First, we analyze LoRa/LoRaWAN and NB-IoT standards and derive realistic constraints on the maximum gap time between two consecutive passing-by satellites. Then, we introduce and optimize an algorithm to design quasioptimal topologies for sparse IoT constellations. Finally, we apply our design to both global and regional coverage and we analyze the trade-off between latency, number of orbit planes and total number of satellites. Results show that sparse constellations can provide world-wide IoT coverage with only 12.5% and 22.5% of the satellites required by traditional dense constellations considering 3-hour and 2-hour gaps. Also, we show that regionspecific coverage of Africa and Europe can be achieved with only 4 and 3 satellites for LoRa/LoRaWAN and NB-IoT, respectively.