Appraising connection adequacy involves asking three questions: 1. What is the warrant of the argument? 2. What type of warrant is it? 3. Does the warrant transfer acceptability from the premisePremise to the conclusion? We have identified four types of warrants, each requiring a different method for appraising connection adequacy. Conclusive a priori warrants involve identifying the argument form and whether that form has an interpretation with all true premises and a false conclusion. For arguments with defeasible a posteriori warrants adequate connection means that any relevant variableRelevant variable either poses no rebuttalRebuttal to the warrant, its rebutting value is countered, or its value is too implausible for consideration. Defeasible a priori warrants are either normative or non-normative. For a normative warrant to adequately connect premisePremise to conclusion the value of any relevant variableRelevant variable must be either implausible or not constitute an exception to the moral rule backing the warrant. In the non-normative cases, the burden (of refutation) is on the challenger. In the absence of rebutting evidence, the warrant stands. For example, if one claimsClaim that Case A should be treated like Case B, the burden should be on the challenger to show the cases relevantly dissimilar. A virtually conclusive a posteriori warrant is either backed by a canonical test taking account of all relevant variables and identifying no rebutting values of a relevant variable or is implied by some system of taxonomy.