diff --git a/src/MeasureBase.jl b/src/MeasureBase.jl
index 093793c8..4fc3bf6a 100644
--- a/src/MeasureBase.jl
+++ b/src/MeasureBase.jl
@@ -28,7 +28,7 @@ import Base.iterate
 import ConstructionBase
 using ConstructionBase: constructorof
 using IntervalSets
-using OneTwoMany: secondarg
+using OneTwoMany: firstarg, secondarg
 
 using PrettyPrinting
 const Pretty = PrettyPrinting
diff --git a/src/combinators/bind.jl b/src/combinators/bind.jl
index a70f27eb..fe6af2bf 100644
--- a/src/combinators/bind.jl
+++ b/src/combinators/bind.jl
@@ -30,12 +30,6 @@ See also [`mbind`](@ref).
 function mkernel end
 export mkernel
 
-@inline mkernel(f_β::MKernel) = f_β
-@inline mkernel(f_β, f_c = secondarg) = _generic_mkernel_impl(f_β, f_c)
-
-@inline _generic_mkernel_impl(f_β, f_c) = MKernel(f_β, f_c)
-@inline _generic_mkernel_impl(f_β::MKernel, ::typeof(secondarg)) = f_β
-
 
 """
     struct MeasureBase.MKernel <: Function
@@ -45,12 +39,20 @@ Represents a generalized monatic transition kernel.
 User code should not create instances of `MKernel` directly, but should call
 [`mkernel`](@ref) instead.
 """
-struct MKernel
-    f_β::FK
+struct MKernel{FT,FC} <: Function
+    f_β::FT
     f_c::FC
 end
 
 
+@inline mkernel(f_β::MKernel) = f_β
+@inline mkernel(f_β, f_c = secondarg) = _generic_mkernel_impl(f_β, f_c)
+
+@inline _generic_mkernel_impl(f_β, f_c) = MKernel(f_β, f_c)
+@inline _generic_mkernel_impl(f_β::MKernel, ::typeof(secondarg)) = f_β
+
+
+
 @doc raw"""
     mbind(f_β, α::AbstractMeasure, f_c = OneTwoMany.secondarg)
     mbind(f_β::MeasureBase.MKernel, α::AbstractMeasure)
@@ -102,7 +104,7 @@ The measure `α` that went into the bind can be retrieved via
 
 Densities on hierarchical measures can only be evaluated if `ab = f_c(a, b)`
 can be unambiguously split into `a` and `b` again, knowing `α`. This is
-currently implemented for `f_c` that is either tuple or `=>`/`Pair` (these
+currently implemented for `f_c` that is either `tuple` or `=>`/`Pair` (these
 work for any combination of variate types), `vcat` (for tuple- or vector-like
 variates) and `merge` (`NamedTuple` variates).
 [`MeasureBase.split_point(::typeof(f_c), α)`](@ref) can be specialized to
@@ -152,19 +154,20 @@ export mbind
 
 @inline mbind(f_β) = Base.Fix1(mbind, f_β)
 
-@inline mbind(f_k::MKernel, α::AbstractMeasure) = mbind(f_k.f_β, α, f_k.f_c)
-
-#@inline mbind(f_β, α::AbstractMeasure, f_c = getsecond) = _generic_mbind_impl(f_β, α, f_c) --- temporary ---
-@inline mbind(f_β, α::AbstractMeasure, f_c = secondarg) = _generic_mbind_impl(f_β, α, f_c)
+@inline mbind(f_β, α::AbstractMeasure, f_c = secondarg) = _generic_mbind_impl(f_β, asmeasure(α), f_c)
 
 @inline function _generic_mbind_impl(f_β, α::AbstractMeasure, f_c)
     F, M, G = Core.Typeof(f_β), Core.Typeof(α), Core.Typeof(f_c)
     Bind{F,M,G}(f_β, α, f_c)
 end
 
-function _generic_mbind_impl(f_β, α::Dirac, f_c)
-    mcombine(f_c, α, f_β(α.x))
-end
+@inline _generic_mbind_impl(f_β, α::Dirac, f_c) = mcombine(f_c, α, f_β(α.x))
+
+@inline _generic_mbind_impl(@nospecialize(f_β), α::AbstractMeasure, ::typeof(firstarg)) = α
+@inline _generic_mbind_impl(@nospecialize(f_β), α::Dirac, ::typeof(firstarg)) = α
+
+@inline _generic_mbind_impl(f_k::MKernel, α::AbstractMeasure, ::typeof(secondarg)) = mbind(f_k.f_β, α, f_k.f_c)
+@inline _generic_mbind_impl(f_k::MKernel, α::Dirac, ::typeof(secondarg)) = mbind(f_k.f_β, α, f_k.f_c)
 
 
 """
@@ -175,8 +178,8 @@ Represents a monatic bind resp. a mbind in general.
 User code should not create instances of `Bind` directly, but should call
 [`mbind`](@ref) instead.
 """
-struct Bind{FK,M<:AbstractMeasure,FC} <: AbstractMeasure
-    f_β::FK
+struct Bind{FT,M<:AbstractMeasure,FC} <: AbstractMeasure
+    f_β::FT
     α::M
     f_c::FC
 end
diff --git a/src/combinators/combined.jl b/src/combinators/combined.jl
index 11ebc558..4127e952 100644
--- a/src/combinators/combined.jl
+++ b/src/combinators/combined.jl
@@ -62,9 +62,8 @@ export mcombine
 
 @inline mcombine(f_c, α::AbstractMeasure, β::AbstractMeasure) = _generic_mcombine_impl_stage1(f_c, α, β)
 
-@inline _generic_mcombine_impl_stage1(::typeof(first), α::AbstractMeasure, β::AbstractMeasure) = α
-@inline _generic_mcombine_impl_stage1(::typeof(getsecond), α::AbstractMeasure, β::AbstractMeasure) = β
-@inline _generic_mcombine_impl_stage1(::typeof(last), α::AbstractMeasure, β::AbstractMeasure) = β
+@inline _generic_mcombine_impl_stage1(::typeof(firstarg), α::AbstractMeasure, β::AbstractMeasure) = α
+@inline _generic_mcombine_impl_stage1(::typeof(secondarg), α::AbstractMeasure, β::AbstractMeasure) = β
 
 @inline function _generic_mcombine_impl_stage1(::typeof(tuple), α::AbstractMeasure, β::AbstractMeasure)
     productmeasure((α, β))