Spinodal demixing was initiated in two systems, with critical and off-critical compositions, using nanosecond pulsed laser-induced temperature jumps (T-jumps) of various magnitude. In this way, deep quenches could be imposed on the systems. One system was the simple triethylamine (TEA)/water mixture and the other was the ionic mixture of 2-butoxyethanol (2BE)/water/KCl. The demixing process was followed using the technique of nanosecond time-resolved microscopic shadowgraphy. The growth of the evolving phase-separated domains followed a simple power law with respect to time in every case. For a given composition, the magnitude of the T-jump had little effect on the growth exponent, however the composition was found to influence the rate of domain growth. At off-critical mole fractions of 0.2 with respect to TEA, the domains grew according to the following expression: L(t) = t0.70 (where L(t) =the domain size) whereas at the critical TEA mole fraction of 0.08 the domains grew as L(t) = t0.52. 2BE/water/KCl mixtures quenched at the just off-critical composition of 0.05 mole fraction with respect to 2BE evolved as L(t) = t0.63. These results will be compared to theoretical models and simulations and discussed in terms of estimated Reynolds numbers as well as the consumption and conversion of the available surface energy that fuels the demixing process.