Both diastolic filling and systolic pumping of the heart are dependent on the passive stiffness characteristics of various mechanical elements of myocardium. However, the specific contribution from each element, including the extracellular matrix, actin filaments, microtubules, desmin intermediate filaments, and sarcomeric titin springs, remains challenging to assess. Recently, a mouse model allowing for precise and acute cleavage of the titin springs was used to remove one mechanical element after the other from cardiac fibers and record the effect on passive stiffness. It became clear that the stiffness contribution from each element is context-dependent and varies depending on strain level and the force component considered (elastic or viscous); elements do not act in isolation but in a tensegral relationship. Titin is a substantial contributor under all conditions and dominates the elastic forces at both low and high strains. The contribution to viscous forces is more equally shared between microtubules, titin, and actin. However, the extracellular matrix substantially contributes to both force components at higher strain levels. Desmin filaments may bear low stiffness. These insights enhance our understanding of how different filament networks contribute to passive stiffness in the heart and offer new perspectives for targeting this stiffness in heart failure treatment.