The conditions required for the production of isolated attosecond pulses from relativistically oscillating mirrors (ROM) are investigated numerically and experimentally. In simulations, carrier-envelope-phase-stabilized three-cycle pulses are found to be sufficient to produce isolated attosecond pulses, while two-cycle pulses will predominantly lead to isolated attosecond pulses even in the absence of carrier-envelope stabilization. Using a state-of-the-art laser system delivering three-cycle pulses at multiple-terawatt level, we have generated higher harmonics up to 70 eV photon energy via the ROM mechanism. The observed spectra are in agreement with theoretical expectations and highlight the potential of few-cycle-driven ROM harmonics for intense isolated attosecond pulse generation for performing extreme ultraviolet-pump extreme ultraviolet-probe experiments.