Rob McConnell (1935-2010) was a Canadian trombone player who led his own group, the Big Boss Brass. McConnell played for Rover Joe in the special The Muppet Musicians of Bremen.

McConnell began performing and recording in the 1950s, and would later play with trumpeter Maynard Ferguson. His Big Boss Brass group backed Mel Tormé on recordings. He won three Grammy Awards (one as an artist, two as arranger).

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