We introduce a design strategy to expand the range of accessible mechanical properties in covalent adaptable networks (CANs) using bottlebrush polymer building blocks. Well-defined bottlebrush polymers with rubbery poly(4-methylcaprolactone) side chains were cross-linked in formulations that include a bislactone and strong Lewis acid (tin ethylhexanoate). The resulting materials exhibit tunable stress-relaxation rates at elevated temperatures (160-180 degrees C) due to dynamic ester cross-links that undergo transesterification with residual hydroxy groups. Varying the cross-linker loading or bottlebrush backbone degree of polymerization yields predictable low-frequency shear moduli ca. 10-100 kPa, well below values typical of linear polymer CANs (1 MPa). These extensible networks can be stretched to strains as large as 350% before failure and undergo efficient self-healing to recover >85% of their original toughness upon repeated fracture and melt processing. In summary, molecular architecture creates new opportunities to tailor the mechanical properties of CANs in ways that are otherwise difficult to achieve.