Background: Reliable estimation of excess mortality is central to population health surveillance. We introduce NeMMo (New Mortality Model), an evolution of the EuroMOMO model for estimating weekly all-cause expected mortality, and assess its behaviour and performance on empirical data. Methods: NeMMo incorporates population offsets, stratifies observed deaths by age group and models seasonality using a periodic B-spline rather than a Serfling-type sinusoidal function. Baseline weeks are selected by a data-driven procedure minimizing the skewness of the residuals before refitting the model, instead of relying solely on fixed calendar windows. NeMMo enables pooling across age groups, direct age standardization and incorporation of external predictors. We applied NeMMo and EuroMOMO to mortality and population data downloaded from Eurostat for 31 countries from 2015 onwards, excluding the COVID-19 pandemic period from baseline estimation. Results: For most countries NeMMo produced a higher expected mortality baseline that better tracked observed deaths, as well as tighter prediction intervals and higher maximum Z-scores, suggesting improved discrimination of mortality excesses. Z-scores and P-scores during non-pandemic weeks were closer to zero with NeMMo than with EuroMOMO but further elevated during pandemic weeks, providing greater separation between pandemic and non-pandemic mortality. Incorporating population offsets resulted in negative linear trends across all countries, consistent with declining mortality after accounting for demographic changes. The periodic B-spline identified substantial heterogeneity in the shape and timing of seasonal mortality that was not captured by a sinusoidal function. Conclusions: NeMMo provides a flexible and parsimonious framework for all-cause mortality surveillance that improves the established EuroMOMO model and offers theoretical, empirical and practical advantages. It is thus suitable both for detecting short-term spikes and for the long-term, age-adjusted quantification and comparison of mortality excesses that has become increasingly important since the COVID-19 pandemic. The accompanying 'nemmo' package for R facilitates its widespread adoption and application.