This is a Phase 2, randomized, double-blind, placebo-controlled, ascending starting dose finding study assessing safety, efficacy, tolerability and PK of BXCL501 in four starting dose cohort groups to reduce agitation levels associated with delirium in patients within the ICU setting. Evaluation of four BXCL501 starting doses compared to placebo will be conducted according to the following ascending doses: Cohort 1 (120 μg or placebo); Cohort 2 (180 μg or placebo); Cohort 3 (240 μg or placebo); Cohort 4 (300 μg or placebo). For subjects 65 years of age and older, the starting doses in each cohort will be reduced 50% in line with the Precedex (reference drug) label. Safety, efficacy, and tolerability will be assessed throughout the treatment period at various timepoints. Subjects will receive the first starting dose (BXCL501 or placebo) when Baseline RASS score is ≥ +1. Repeat doses may be administered in increments of 120 μg every 3 to 6 hours post first dose (StartD) only if the RASS score remains ≥ +1. For subjects 65 years and older, repeat doses may start in increments of 60 μg every 3 to 6 hours post first dose only if RASS is still ≥+1.