diff --git a/src/multivariate/mvnormal.jl b/src/multivariate/mvnormal.jl
index 63888f01aa..82d4c71999 100644
--- a/src/multivariate/mvnormal.jl
+++ b/src/multivariate/mvnormal.jl
@@ -397,9 +397,9 @@ fit_mle(D::Type{MvNormal}, ss::MvNormalStats) = fit_mle(FullNormal, ss)
 fit_mle(D::Type{MvNormal}, x::AbstractMatrix{Float64}) = fit_mle(FullNormal, x)
 fit_mle(D::Type{MvNormal}, x::AbstractMatrix{Float64}, w::AbstractArray{Float64}) = fit_mle(FullNormal, x, w)
 
-fit_mle(D::Type{FullNormal}, ss::MvNormalStats) = MvNormal(ss.m, ss.s2 * inv(ss.tw))
+fit_mle(D::Type{<:FullNormal}, ss::MvNormalStats) = MvNormal(ss.m, ss.s2 * inv(ss.tw))
 
-function fit_mle(D::Type{FullNormal}, x::AbstractMatrix{Float64})
+function fit_mle(D::Type{<:FullNormal}, x::AbstractMatrix{Float64})
     n = size(x, 2)
     mu = vec(mean(x, dims=2))
     z = x .- mu
@@ -408,7 +408,7 @@ function fit_mle(D::Type{FullNormal}, x::AbstractMatrix{Float64})
     MvNormal(mu, PDMat(C))
 end
 
-function fit_mle(D::Type{FullNormal}, x::AbstractMatrix{Float64}, w::AbstractVector)
+function fit_mle(D::Type{<:FullNormal}, x::AbstractMatrix{Float64}, w::AbstractVector)
     m = size(x, 1)
     n = size(x, 2)
     length(w) == n || throw(DimensionMismatch("Inconsistent argument dimensions"))
@@ -428,7 +428,7 @@ function fit_mle(D::Type{FullNormal}, x::AbstractMatrix{Float64}, w::AbstractVec
     MvNormal(mu, PDMat(C))
 end
 
-function fit_mle(D::Type{DiagNormal}, x::AbstractMatrix{Float64})
+function fit_mle(D::Type{<:DiagNormal}, x::AbstractMatrix{Float64})
     m = size(x, 1)
     n = size(x, 2)
 
@@ -443,7 +443,7 @@ function fit_mle(D::Type{DiagNormal}, x::AbstractMatrix{Float64})
     MvNormal(mu, PDiagMat(va))
 end
 
-function fit_mle(D::Type{DiagNormal}, x::AbstractMatrix{Float64}, w::AbstractVector)
+function fit_mle(D::Type{<:DiagNormal}, x::AbstractMatrix{Float64}, w::AbstractVector)
     m = size(x, 1)
     n = size(x, 2)
     length(w) == n || throw(DimensionMismatch("Inconsistent argument dimensions"))
@@ -462,7 +462,7 @@ function fit_mle(D::Type{DiagNormal}, x::AbstractMatrix{Float64}, w::AbstractVec
     MvNormal(mu, PDiagMat(va))
 end
 
-function fit_mle(D::Type{IsoNormal}, x::AbstractMatrix{Float64})
+function fit_mle(D::Type{<:IsoNormal}, x::AbstractMatrix{Float64})
     m = size(x, 1)
     n = size(x, 2)
 
@@ -478,7 +478,7 @@ function fit_mle(D::Type{IsoNormal}, x::AbstractMatrix{Float64})
     MvNormal(mu, ScalMat(m, va / (m * n)))
 end
 
-function fit_mle(D::Type{IsoNormal}, x::AbstractMatrix{Float64}, w::AbstractVector)
+function fit_mle(D::Type{<:IsoNormal}, x::AbstractMatrix{Float64}, w::AbstractVector)
     m = size(x, 1)
     n = size(x, 2)
     length(w) == n || throw(DimensionMismatch("Inconsistent argument dimensions"))
diff --git a/test/multivariate/mvnormal.jl b/test/multivariate/mvnormal.jl
index 4af9275b3f..e2160491ce 100644
--- a/test/multivariate/mvnormal.jl
+++ b/test/multivariate/mvnormal.jl
@@ -239,6 +239,15 @@ end
     @test isa(g, DiagNormal)
     @test g.μ      ≈ uw
     @test g.Σ.diag ≈ diag(Cw)
+
+    # fit_mle should accept the aliases in instantiated or fully concrete form,
+    # not just as the bare `UnionAll` name (#2073 regression)
+    for A in (FullNormal, DiagNormal, IsoNormal)
+        g = fit_mle(A, x)
+        @test fit_mle(A{Float64}, x) == g          # instantiated alias
+        @test fit_mle(typeof(g), x) == g           # concrete member type
+        @test fit_mle(A{Float64}, x, w) == fit_mle(A, x, w)
+    end
 end
 
 @testset "MvNormal affine transformations" begin