They took a major step toward alleviating that problem at the 1987 NBA draft, when Vice President of Basketball Operations Jerry Krause acquired two players who would be vital cogs in Chicago's future championship machine.
Chicago finished in a second-place tie with Atlanta in a competitive Central Division won by the surging Detroit Pistons.
The Bulls made some noise in the playoffs, defeating the Cleveland Cavaliers in a five-game first-round series, but then fell to Detroit in the Eastern Conference semifinals.
Oakley and the Los Angeles Clippers' Michael Cage engaged in a nip-and-tuck battle for the league's rebounding title, which came down to the last day of the regular season.
On April 22 against Cleveland, Oakley put the pressure on Cage by pulling down 35 rebounds, the second-highest total in Bulls history behind Tom Boerwinkle's 37 in 1970.