Givens was known most for being a replacement player who crossed picket lines during spring training in 1995 while the 1994–95 Major League Baseball strike was still going on.

[4] The following year, Givens pitched for the Mets for the entire season, posting an 8–7 record with a 3.77 earned-run average in 27 games.

[4] In 1987, Givens actually briefly rose to the Triple-A International League level, pitching for one game with the Tidewater Tides (and posting a 0–1 mark with a 24.55 earned-run average from that one game; his outing lasted just three and two-thirds innings) but spending almost the entire season at the "High-A" level with the Lynchburg Hillcats.

[4] In 1988, Givens spent the entire season with the Jackson Mets in the Class AA Texas League, going 6–14 with a 3.78 earned-run average in 26 games.

[4] During the season, however, Givens' elbow popped, requiring a surgery to move his ulnar nerve and taking five miles an hour off his fastball.

[4] He also pitched for one game in 1989 with the St. Lucie Mets in the High-A Florida State League, posting an 0–1 mark with no earned-run average in a five-inning stint.

[5] In early 1992, Givens developed a tender spot on the outside of his elbow, opposite of the surgery, requiring arthroscopy.

[2] He pitched in seven games for the Memphis Chicks, who at that time were the Royals' Class AA minor-league club in the Southern League.

Givens posted no record and a 3.24 earned-run average, and wound up needing another arthroscopy to remove four large chips.

"[5] After the 234-day players strike ended in before the 1995 baseball season ever officially began, Givens was sent to the Brewers' Class AAA New Orleans Zephyrs ballclub, where he worked with pitching coach and former major-league relief pitcher Bill Campbell, who taught Givens a slider and helped him to improve his changeup.

[5] After pitching well with New Orleans, where he posted a 7–4 record and a 2.55 earned-run average in 16 games, Givens was promoted to the Brewers.

As had been the case with his teammate Ron Rightnowar, there was some bitterness toward Givens by the major-leaguers because of his role as a replacement player.

"I've spent 11½ years in the minor leagues, I have a mortgage and two kids to feed", he told the Sporting News in 1995.

"I would have sent him back to the minor leagues if I had somebody else to replace him with", the Brewers' manager, Phil Garner, told the Sporting News.

[2] He had begun the season on a 30-day rehabilitation assignment with New Orleans after injuring his back in his final throwing session at home in Aurora, Colorado the day before he left for 1996 spring training.

[9] After his 30-day rehab assignment, Givens unexpectedly ended up staying longer in AAA instead of being promoted to the major leagues.

[11] He filed for free agency on October 15, 1996, after he and the Brewers decided to part ways by mutual agreement.

[13] In 1998, Givens returned to North America, pitching for the Shreveport Captains in the Double-A Texas League.