Using two infrared pulsed lasers systems, a picosecond solid-state Nd:YAG laser with tuneable repetition rate (400 kHz–1 MHz) working in the burst mode of a multi-pulse train and a femtosecond Ti:sapphire laser amplifier with tuneable pulse duration in the range of tens of femtoseconds up to tens of picoseconds, working in single-shot mode (TEWALASS facility from CETAL-NILPRP), we have investigated the optimal laser parameters for kinetic energy transfer to a titanium target for laser-thrust applications. In the single-pulse regime, we controlled the power density by changing both the duration and pulse energy. In the multi-pulse regime, the train’s number of pulses (burst length) and the pulse energy variation were investigated. Heat propagation and photon reflection-based models were used to simulate the obtained experimental results. In the single-pulse regime, optimal kinetic energy transfer was obtained for power densities of about 500 times the ablation threshold corresponding to the specific laser pulse duration. In multi-pulse regimes, the optimal number of pulses per train increases with the train frequency and decreases with the pulse power density. An ideal energy transfer efficiency resulting from our experiments and simulations is close to about 0.0015%.