Firefly Algorithm (FA) is a recent and promising swarm intelligence algorithm. It is inspired by the modelling of brightness and attractiveness manifested by fireflies. Like other population-based algorithms, it presents the drawbacks of high computational cost and memory storage. This paper deals with this problem and introduces a compact firefly optimisation technique with minimal computational and memory requirements. So, we present four new variants of compact firefly algorithm that require only a minimal computational cost. The swarm is compacted and represented by a Probability of Density Function (PDF). This idea is inspired from compact evolutionary algorithms (cEAs). Two solutions of memory storage of the population are presented and analysed. The first is based on normal PDF and the second on uniform PDF. Furthermore, two versions of compact Lévy-flight firefly algorithm (cLFA) are also introduced. This paper takes a step towards new compact swarm intelligence algorithms. The proposed algorithms are compared to the state-of-art of cEAs and two original variants of FA using IEEE CEC2014 functions. In addition, the proposed algorithms are used to realise an optimal swing-up movement of a humanoid robot hanging on a bar.