High harmonic generation (HHG) using waveform-controlled, few-cycle pulses from Ti:sapphire lasers has opened emerging researches in strong-field and attosecond physics. However, the maximum photon energy of attosecond pulses via HHG remains limited to the extreme ultraviolet region. Long-wavelength light sources with carrier-envelope phase stabilization are promising to extend the photon energy of attosecond pulses into the soft X-ray region. Here we demonstrate carrier-envelope phase-dependent HHG in the water window using sub-two-cycle optical pulses at 1,600 nm. Experimental and simulated results indicate the confinement of soft X-ray emission in a single recombination event with a bandwidth of 75 eV around the carbon K edge. Control of high harmonics by the waveform of few-cycle infrared pulses is a key milestone to generate soft X-ray attosecond pulses. We measure a dependence of half-cycle bursts on the gas pressure, which indicates subcycle deformation of the waveform of the infrared drive pulses in the HHG process.