When designing a new type of power plants operating on pulsed detonations of gaseous or liquid fuels, the concept of fast deflagration-to-detonation transition (FDDT) is used. According to the concept, a flame arising from a weak ignition source must accelerate so fast as to form an intense shock wave at a minimum distance from the ignition source so that the intensity of the shock wave is sufficient for fast shock-to-detonation transition by some additional arrangements. Hence, the FDDT concept implies the use of special means for flame acceleration and shock wave amplification. In this work, we study the FDDT using a pulsed detonation tube comprising a Shchelkin spiral and a helical tube section with ten coils as the means for flame acceleration and shock amplification (focusing), respectively. To attain the FDDT at the shortest distances for fuels of significantly different detonability, the diameter of the pulsed detonation tube is taken close to the limiting diameter of detonation propagation for air mixtures of regular hydrocarbon fuels (50 mm). Experiments are conducted with air mixtures of individual gaseous fuels (hydrogen, methane, propane, and ethylene) and binary fuel compositions (methane−hydrogen, propane−hydrogen, and ethylene−hydrogen) at normal pressure and temperature conditions. The use of a helical tube with ten coils is shown to considerably extend the fuel-lean concentration limits of detonation as compared to the straight tube and the tube with a helical section with two coils.