Quantum metrology exploits quantum correlations to make precise measurements with limited particle numbers. By maximising the inter- and intra- mode correlations in an optical interferometer, we find a state that combines squeezing and entanglement to give a 7-fold enhancement in the quantum Fisher information (QFI) over the NOON state for low photon numbers. Motivated by practicality we then look at the squeezed cat state, which has recently been made experimentally, and shows further precision gains, including a 3-fold improvement in the QFI over the optimal Gaussian state. We present a simple measurement scheme that saturates the QFI, and then simulate this scheme to confirm its effectiveness. Finally, we show that for small photon numbers the squeezed cat state continues to give an advantage even for significant losses, allowing us to conclude that the squeezed cat state can give a significant precision enhancement in optical quantum metrology in realistic conditions.