Gluten strength and gluten extensibility influence both pasta-making and bread-making qualities of durum wheat. This study examined the relationship among various gluten quality-related screening parameters. It also determined (using stepwise regression analysis) which screening parameters were more suitable to predict gluten strength (alveographic parameters ALVW and ALVPL) and bread loaf volume (LV). The experimental material used was practically all (152 of 156 samples) of the LMW-2 glutenin type and it included conventional and exotic durum wheat germplasm from CIMMYT. In addition, the relationship between various Glu-B1-controlled HMW-glutenin subunits and gluten quality-related parameters was determined. Gluten Index (GLUIND), grain SDS-sedimentation (GRNSED), and Mixograph curve width (MWP3), were highly significantly correlated with ALVW and bread LV. To breed for medium to strong gluten types, breeders should avoid, in addition to LMW-1 type glutenins, HMW-glutenin subunit 20.