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Maps of the transverse relaxation rate R 2 * and magnetic susceptibility ( χ ) are computed from gradient‐echo data and are sensitive to signal instabilities induced by cardiac pulsation. Here, we introduce two k‐space sampling strategies that aim to mitigate the impact of cardiac‐induced noise in brain maps of R 2 * and χ . The proposed strategies are based on the higher level of cardiac‐induced noise near the k‐space centre compared to the periphery. Using CArtesian trajectory with Spiral PRofile (CASPR), the first strategy allows for the acquisition of a specific number of averages at each k‐space location, derived from the local level of cardiac‐induced noise. The second strategy uses cardiac triggering to synchronize the acquisition near the k‐space centre with the cardiac cycle in real time. We compared the variability across four repetitions of R 2 * and χ maps computed from data acquired using both strategies and with a standard linear trajectory. Data were acquired in 10 healthy volunteers. Compared to linear trajectory, CASPR reduced the variability of R 2 * and χ maps across repetitions by 22% and 16% across the whole brain, reaching over 30% in inferior brain regions, for a 14% increase in scan time. CASPR also reduced the level of aliasing artefacts from pulsating blood vessels. Cardiac triggering did not reduce the variability of R 2 * or χ maps. CASPR can be designed to mitigate cardiac‐induced noise in brain maps of the MRI parameters R 2 * and χ . Synchronization of data acquisition with the cardiac cycle did not reduce the level of cardiac‐induced noise.