<p>In this essay, I prove two general recapture theorems (the <b>GRT</b> and the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textbf{GRT}^\textsf{Dual}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="bold">GRT</mi> <mi mathvariant="sans-serif">Dual</mi> </msup> </math></EquationSource> </InlineEquation>). Each of these states that any sub-logic of classical logic that is closed under six rules of inference is equivalent, in the relevant sense, to classical logic. After proving in each case that the six rules in question are independent of one another, and exploring a number of possible modifications or extensions of these results, I compare the results to <span>Jc</span> Beall’s recapture results in Beall (<CitationRef CitationID="CR2">2011</CitationRef>), Beall (<CitationRef CitationID="CR3">2013a</CitationRef>) and Beall (<CitationRef CitationID="CR4">2013b</CitationRef>). The <b>GRT</b> (and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textbf{GRT}^\textsf{Dual}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="bold">GRT</mi> <mi mathvariant="sans-serif">Dual</mi> </msup> </math></EquationSource> </InlineEquation>) are shown to be more powerful and general than Beall’s more piecemeal approach.</p>