diff --git a/src/combinators/power.jl b/src/combinators/power.jl
index 1bc17866..37797d85 100644
--- a/src/combinators/power.jl
+++ b/src/combinators/power.jl
@@ -12,9 +12,14 @@ using FillArrays: Fill
 
 export PowerMeasure
 
-struct PowerMeasure{M,A} <: AbstractProductMeasure
+struct PowerMeasure{M,N,A} <: AbstractProductMeasure{Fill{M,N,A}}
     parent::M
     axes::A
+
+    function PowerMeasure(parent::M, axes::A) where {M,A}
+        N = length(axes)
+        new{M,N,A}(parent, axes)
+    end
 end
 
 function Pretty.tile(μ::PowerMeasure)
@@ -42,8 +47,7 @@ end
 
 @inline function powermeasure(x::T, sz::Tuple{Vararg{<:Any,N}}) where {T,N}
     a = axes(Fill{T,N}(x, sz))
-    A = typeof(a)
-    PowerMeasure{T,A}(x, a)
+    PowerMeasure(x, a)
 end
 
 marginals(d::PowerMeasure) = Fill(d.parent, d.axes)
@@ -76,7 +80,14 @@ end
 end
 
 @inline function logdensity_def(
-    d::PowerMeasure{M,Tuple{Base.OneTo{StaticInt{N}}}},
+    d::PowerMeasure{M,1,Tuple{Base.OneTo{StaticInt{0}}}},
+    x,
+) where {M}
+   static(0.0)
+end
+
+@inline function logdensity_def(
+    d::PowerMeasure{M,1,Tuple{Base.OneTo{StaticInt{N}}}},
     x,
 ) where {M,N}
     parent = d.parent
@@ -86,7 +97,7 @@ end
 end
 
 @inline function logdensity_def(
-    d::PowerMeasure{M,NTuple{N,Base.OneTo{StaticInt{0}}}},
+    d::PowerMeasure{M,N,NTuple{N,Base.OneTo{StaticInt{0}}}},
     x,
 ) where {M,N}
     static(0.0)
@@ -108,7 +119,8 @@ end
     end
 end
 
-@inline getdof(μ::PowerMeasure) = getdof(μ.parent) * prod(map(length, μ.axes))
+# `prod` isn't static-friendly
+@inline getdof(μ::PowerMeasure) = getdof(μ.parent) * (*(map(length, μ.axes)...))
 
 @inline function getdof(::PowerMeasure{<:Any,NTuple{N,Base.OneTo{StaticInt{0}}}}) where {N}
     static(0)
diff --git a/src/combinators/product.jl b/src/combinators/product.jl
index cb7a0aaf..bbe96513 100644
--- a/src/combinators/product.jl
+++ b/src/combinators/product.jl
@@ -8,7 +8,7 @@ using FillArrays
 
 export AbstractProductMeasure
 
-abstract type AbstractProductMeasure <: AbstractMeasure end
+abstract type AbstractProductMeasure{M} <: AbstractMeasure end
 
 function Pretty.tile(μ::AbstractProductMeasure)
     result = Pretty.literal("ProductMeasure(")
@@ -76,7 +76,7 @@ end
     mapreduce(logdensity_def, +, marginals(d), x)
 end
 
-struct ProductMeasure{M} <: AbstractProductMeasure
+struct ProductMeasure{M} <: AbstractProductMeasure{M}
     marginals::M
 end
 
diff --git a/src/standard/stdmeasure.jl b/src/standard/stdmeasure.jl
index 2b50c1e5..34d7e4d8 100644
--- a/src/standard/stdmeasure.jl
+++ b/src/standard/stdmeasure.jl
@@ -17,16 +17,16 @@ function transport_def(ν::PowerMeasure{<:StdMeasure}, μ::StdMeasure, x)
 end
 
 function transport_def(
-    ν::PowerMeasure{<:StdMeasure,<:NTuple{1,Base.OneTo}},
-    μ::PowerMeasure{<:StdMeasure,<:NTuple{1,Base.OneTo}},
+    ν::PowerMeasure{<:StdMeasure,1,<:NTuple{1,Base.OneTo}},
+    μ::PowerMeasure{<:StdMeasure,1,<:NTuple{1,Base.OneTo}},
     x,
 )
     return transport_to(ν.parent, μ.parent).(x)
 end
 
 function transport_def(
-    ν::PowerMeasure{<:StdMeasure,<:NTuple{N,Base.OneTo}},
-    μ::PowerMeasure{<:StdMeasure,<:NTuple{M,Base.OneTo}},
+    ν::PowerMeasure{<:StdMeasure,N,<:NTuple{N,Base.OneTo}},
+    μ::PowerMeasure{<:StdMeasure,M,<:NTuple{M,Base.OneTo}},
     x,
 ) where {N,M}
     return reshape(transport_to(ν.parent, μ.parent).(x), map(length, ν.axes)...)
@@ -72,7 +72,7 @@ end
 
 function transport_def(
     ν::PowerMeasure{NU},
-    μ::ProductMeasure{<:Tuple},
+    μ::AbstractProductMeasure{<:Tuple},
     x,
 ) where {NU<:StdMeasure}
     _tuple_transport_def(ν, marginals(μ), x)
@@ -80,7 +80,7 @@ end
 
 function transport_def(
     ν::PowerMeasure{NU},
-    μ::ProductMeasure{<:NamedTuple{names}},
+    μ::AbstractProductMeasure{<:NamedTuple{names}},
     x,
 ) where {NU<:StdMeasure,names}
     _tuple_transport_def(ν, values(marginals(μ)), values(x))
@@ -107,7 +107,7 @@ function _tuple_transport_def(
 end
 
 function transport_def(
-    ν::ProductMeasure{<:Tuple},
+    ν::AbstractProductMeasure{<:Tuple},
     μ::PowerMeasure{MU},
     x,
 ) where {MU<:StdMeasure}
@@ -115,7 +115,7 @@ function transport_def(
 end
 
 function transport_def(
-    ν::ProductMeasure{<:NamedTuple{names}},
+    ν::AbstractProductMeasure{<:NamedTuple{names}},
     μ::PowerMeasure{MU},
     x,
 ) where {MU<:StdMeasure,names}