This study aimed to compare four constructs from the three-minute all-out test (AO3)-end power (EP), the area above EP (WEP), maximum power (Pmax), and attained [Formula: see text]-to those derived from the classical CP model in tethered running. Seventeen male recreational runners underwent two experiments to test for reliability and agreement of AO3 parameters with those obtained from the classical CP model (Wꞌ and CP), a graded exercise test ([Formula: see text]) and a 30-second all-out test (AO30s; Pmax); all performed on a non-motorized treadmill (NMT). Significance levels were set at p<0.05. There were no significant differences between test-retest for Pmax (p = 0.51), WEP (p = 0.39), and EP (p = 0.64), showing generally close to zero bias. Further, retest ICC were high for Pmax and EP (ICC > 0.86) but moderate for WEP (ICC = 0.69). Pmax showed no difference between AO3 and AO30s (p = 0.18; CV% = 9.5%). EP and WEP disagreed largely with their classical critical power model counterparts (p = 0.05; CV%>32.7% and p = 0.23; CV%>39.7%, respectively), showing greater error than their test-retest reliability. [Formula: see text] from AO3 was not different (p = 0.13) and well related (CV% = 8.4; ICC = 0.87) to the incremental test [Formula: see text]. Under the studied conditions, the agreement of EP and WEP to CP and Wꞌ was not strong enough to assure their use interchangeably. Pmax and [Formula: see text] were closer to their criterion parameters.