A new Brønsted acidic aluminosilicate, AlTUD-1, with ideal characteristics for catalyst immobilisation (mesoporous structure, high surface area, and high Al(tetrahedral)/Si ratio), was used successfully for the noncovalent anchoring of two well-established asymmetric hydrogenation catalysts: [Rh(I)(cod)[(R,R)-MeDuPHOS]]BF4 (1) and [Rh(I)(cod)[(S,S)-DiPAMP]]BF4 (2). The new heterogeneous catalysts, 1-AlTUD-1 and 2-AlTUD-1, prepared by a straightforward ion-exchange procedure, were highly active and selective in the asymmetric reduction of dimethyl itaconate (3) and methyl 2-acetamidoacrylate (4), giving enantiomeric excesses of up to >98%. The catalysts showed similar behaviour to their homogeneous counterparts. Catalyst 2-AlTUD-1 could be re-used multiple times without loss of enantioselectivity or activity. Leaching of Rh showed a significant dependence on the polarity of the solvent in which the catalysis was performed. By applying tert-butylmethyl ether (MTBE) as solvent, the loss of Rh could be reduced to <0.1%. The solvent also had a noteworthy effect on the enantioselectivity in the hydrogenation of 4 (an effect not seen with 3 as substrate), that is, in MeOH the ee was 92%, in MTBE it dropped to 26% when using 2-AlTUD-1 as catalyst.