[1] He is married to Lorenia and has three sons, Elmer Jr., Erick, Edward[1] Dessens enjoys fishing and is a Los Angeles Lakers fan.

Dessens stayed with the Diamondbacks until August 2004, when the Los Angeles Dodgers acquired him for a minor leaguer to bolster their bullpen for the stretch run.

That October, Dessens pitched in the postseason for the first and, to date, last time, appearing in one game during the Dodgers' Division Series loss to the St. Louis Cardinals.

In July, the Dodgers reacquired Dessens from the Royals for pitcher Odalis Pérez and two minor leaguers, again to bolster their bullpen.

In March 2007, Dessens was traded from the Dodgers to the Milwaukee Brewers for reserve outfielder Brady Clark and cash.

In January 2008, Dessens signed a minor league contract with the Pittsburgh Pirates, but was released during spring training.

[7] On February 8, 2011, it was reported that Dessens had signed a minor league deal with the San Francisco Giants that included an invitation to spring training.