A series of ring-constrained (N)-methanocarba-5′-uronamide 2,N6-disubstituted adenine nucleosides have been synthesized via Mitsunobu condensation of the nucleobase precursor with a pseudosugar ring containing a 5′-ester functionality. Following appropriate functionalization of the adenine ring, the ester group was converted to the 5′-N-methylamide. The compounds, mainly 2-chloro substituted derivatives, were tested in both binding and functional assays at human adenosine receptors (ARs), and many were found to be highly potent and selective A3AR agonists. Selected compounds were compared in binding to the rat A3AR to assess their viability for testing in rat disease models. The N6-(3-chlorobenzyl) and N6-(3-bromobenzyl) analogues displayed Ki values at the human A3AR of 0.29 and 0.38 nM, respectively. Other subnanomolar affinities were observed for the following N6 derivatives: 2,5-dichlorobenzyl, 5-iodo-2-methoxybenzyl, trans-2-phenyl-1-cyclopropyl, and 2,2-diphenylethyl. Selectivity for the human A3AR in comparison to the A1AR was (fold): the N6-(2,2-diphenylethyl) analogue 34 (1900), the N6-(2,5-dimethoxybenzyl) analogue 26 (1200), the N6-(2,5-dichlorobenzyl) and N6-(2-phenyl-1-cyclopropyl) analogues 20 and 33 (1000), and the N6-(3-substituted benzyl) analogues 17, 18, 28, and 29 (700–900). Typically, even greater selectivity ratios were obtained in comparison with the A2A and A2BARs. The (N)-methanocarba-5′-uronamide analogues were full agonists at the A3AR, as indicated by the inhibition of forskolin-stimluated adenylate cyclase at a concentration of 10 µM. The N6-(2,2-diphenylethyl) derivative was an A3AR agonist in the (N)-methanocarba-5′-uronamide series, although it was an antagonist in the ribose series. Thus, many of the previously known groups that enhance A3AR affinity in the 9-riboside series, including those that reducing intrinsic efficacy, may be adapted to the (N)-methanocarba nucleoside series of full agonists.