In order to mitigate the impacts of the energy crise, the European Union has proposed various measures. For the power sector a directive prescribes a shift of 5% of the demand in 10% of the peak hours, plus a voluntary 10% overall demand reduction. Here we use a power system model to quantify the implications of this policy for the Italian power sector, as it stands today and under the transformation required to meet the climate goals of the Fit-for-55. We find that policymakers would need to incentivize electricity consumption in the middle of the day while discouraging it in the early morning and late afternoon. We also highlight the benefits of the decarbonization strategy in the context of uncertain gas prices: for a gas price at or above 50 euro/MWh, power generation through gas is reduced by more than one third, approaching what needed to comply with the Fit-for-55. Finally, we quantify the value of demand side management strategies to curb fossil resource consumption and to reduce curtailed electricity under a high renewable scenario.