Abstract: We consider (s+1) univariate normal populations with common variance σ² and means μ_i, i=0,1,2,...,s, constrained by the tree order restriction μ₀ ≤ μ_i, i=1,2,...,s. The maximum likelihood estimator of μ₀ is known to diverge to -∞ a.s. as s → ∞ if all means μ_i are bounded and all sample sizes n_i remain finite. However, this is not true if the means are unbounded or more importantly if n₀ increases with s, which is the case of most practical interest. In such cases it can be shown that the m.l.e. of μ₀ is consistent, or at least bounded from below. The consistency of a modified version of a estimator due to Cohen and Sackrowitz (2002) also will be discussed.