gaps concentrate exclusively on the Lindblad and viscous torques (e.g., @fsc_2014; @kmt_2015; @zzh_2018) and neglect how gaps can also deepen because embedded planets consume local disc gas. Exceptions include, e.g., @znh_2011, @dk_2015 [@dk_2017], and @mfv_2019, whose numerical simulations of planet-disc interactions allow for both planetary accretion and planetary torques. Our aim here is to give an elementary and analytic accounting of both effects: to understand, for planets on fixed circular orbits, how Lindblad repulsion and planetary consumption combine to set gap depths. This is a two-way feedback problem—planetary accretion affects the gas density inside the gap, but the density inside the gap determines the rate of planetary accretion (@gc_2019a, [-@gc_2019b]). Accordingly we will calculate how gas giants grow in tandem with their deepening gaps. Much of our analytic framework is the same as that of @tt_2016 and @tmt_2020, who used it to study nascent planets in viscous discs; we will explore both viscous and inviscid discs. The problem of planetary accretion within disc gaps is also a global one insofar as a planet can accrete gas that is brought to it from afar, from regions outside the gap. Thus we will stage our calculations within circumstellar discs that transport mass 