We propose a new approach to improve the precision of astrophysical parameter constraints for the 21cm signal from the epoch of reionisation (EoR). Our method introduces new sets of summary statistics, hereafter ‘evolution compressed’ statistics, which quantify the spectral evolution of the 2D spatial statistics computed at fixed redshift. We defined such compressed statistics for power spectrum (PS), wavelet scattering transforms (WST), and wavelet moments (WM), which also characterise non-Gaussian features. To compare these different statistics, along with the 3D power spectrum, we estimated their Fisher information on three cosmological parameters from an ensemble of simulations of 21cm EoR data, both in noiseless and noisy scenarios using Square Kilometre Array (SKA) noise levels equivalent to 100 and 1000 h of observations. We also compare wavelet statistics, in particular WST, built from standard directional Morlet wavelets, as well as from a set of isotropic wavelets derived from the binning window function of the 2D power spectrum. For the noiseless case, the compressed wavelet statistics give constraints that are up to five times more precise than those obtained from the 3D isotropic power spectrum. At the same time, for 100 h SKA noise, from which it is difficult to extract non-Gaussian features, compressed wavelet statistics still give over 30% tighter constraints. We find that the wavelet statistics with wavelets derived from the power-spectrum binning window function provide the tightest constraints of all the statistics, with the WSTs seemingly performing better than the WMs, in particular when working with noisy data. The findings of this study demonstrate that evolution-compressed statistics extract more information than usual 3D isotropic power-spectra approaches and that our wavelet-based statistics can consistently outmatch power-spectrum-based statistics. When constructing such wavelet-based statistics, we also emphasise the need to choose a set of wavelets with an appropriate spectral resolution concerning the astrophysical process studied.