Robert Edward "Bob" Brookmeyer was an American jazz valve trombonist, pianist, arranger, and composer. Born in Kansas City, Missouri, Brookmeyer first gained widespread public attention as a member of Gerry Mulligan's quartet from 1954 to 1957. He later worked with Jimmy Giuffre, before rejoining Mulligan's Concert Jazz Band. He garnered 8 Grammy Award nominations during his lifetime.

The valve trombone is a brass instrument in the trombone family that has a set of valves to vary the pitch instead of a slide. Although it has been built in sizes from alto to contrabass, it is the tenor valve trombone pitched in B♭ which has seen the most widespread use. The most common valve trombone has three piston valves, and plays just like a trumpet but an octave lower. They are built in either short or long form.