diff --git a/Project.toml b/Project.toml
index 28e854655..ab8caccf4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "KernelFunctions"
 uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
-version = "0.10.19"
+version = "0.10.20"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/docs/src/api.md b/docs/src/api.md
index 7ac2dacc3..c44c51593 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -88,3 +88,12 @@ kernelpdmat
 nystrom
 NystromFact
 ```
+
+## Conditional Utilities
+To keep the dependencies of KernelFunctions lean, some functionality is only available if specific other packages are explicitly loaded (`using`).
+
+### Kronecker.jl
+[*https://github.com/MichielStock/Kronecker.jl*](https://github.com/MichielStock/Kronecker.jl)
+```@docs
+kronecker_kernelmatrix
+```
diff --git a/src/matrix/kernelkroneckermat.jl b/src/matrix/kernelkroneckermat.jl
index 1a25c7618..7ffa6705a 100644
--- a/src/matrix/kernelkroneckermat.jl
+++ b/src/matrix/kernelkroneckermat.jl
@@ -27,31 +27,43 @@ end
 """
 @inline iskroncompatible(κ::Kernel) = false # Default return for kernels
 
-function _kernelmatrix_kroneckerjl_helper(::MOInputIsotopicByFeatures, Kfeatures, Koutputs)
+function _kernelmatrix_kroneckerjl_helper(
+    ::Type{<:MOInputIsotopicByFeatures}, Kfeatures, Koutputs
+)
     return Kronecker.kronecker(Kfeatures, Koutputs)
 end
 
-function _kernelmatrix_kroneckerjl_helper(::MOInputIsotopicByOutputs, Kfeatures, Koutputs)
+function _kernelmatrix_kroneckerjl_helper(
+    ::Type{<:MOInputIsotopicByOutputs}, Kfeatures, Koutputs
+)
     return Kronecker.kronecker(Koutputs, Kfeatures)
 end
 
+"""
+    kronecker_kernelmatrix(
+        k::Union{IndependentMOKernel,IntrinsicCoregionMOKernel}, x::MOI, y::MOI
+    ) where {MOI<:IsotopicMOInputsUnion}
+
+Requires Kronecker.jl: Computes the `kernelmatrix` for the `IndependentMOKernel` and the
+`IntrinsicCoregionMOKernel`, but returns a lazy kronecker product. This object can be very
+efficiently inverted or decomposed. See also [`kernelmatrix`](@ref).
+"""
 function kronecker_kernelmatrix(
-    k::Union{IndependentMOKernel,IntrinsicCoregionMOKernel},
-    x::IsotopicMOInputsUnion,
-    y::IsotopicMOInputsUnion,
-)
-    @assert x.out_dim == y.out_dim
+    k::Union{IndependentMOKernel,IntrinsicCoregionMOKernel}, x::MOI, y::MOI
+) where {MOI<:IsotopicMOInputsUnion}
+    x.out_dim == y.out_dim ||
+        throw(DimensionMismatch("`x` and `y` must have the same `out_dim`"))
     Kfeatures = kernelmatrix(k.kernel, x.x, y.x)
     Koutputs = _mo_output_covariance(k, x.out_dim)
-    return _kernelmatrix_kroneckerjl_helper(x, Kfeatures, Koutputs)
+    return _kernelmatrix_kroneckerjl_helper(MOI, Kfeatures, Koutputs)
 end
 
 function kronecker_kernelmatrix(
-    k::Union{IndependentMOKernel,IntrinsicCoregionMOKernel}, x::IsotopicMOInputsUnion
-)
+    k::Union{IndependentMOKernel,IntrinsicCoregionMOKernel}, x::MOI
+) where {MOI<:IsotopicMOInputsUnion}
     Kfeatures = kernelmatrix(k.kernel, x.x)
     Koutputs = _mo_output_covariance(k, x.out_dim)
-    return _kernelmatrix_kroneckerjl_helper(x, Kfeatures, Koutputs)
+    return _kernelmatrix_kroneckerjl_helper(MOI, Kfeatures, Koutputs)
 end
 
 function kronecker_kernelmatrix(
diff --git a/src/mokernels/independent.jl b/src/mokernels/independent.jl
index 647b29373..1f7811b14 100644
--- a/src/mokernels/independent.jl
+++ b/src/mokernels/independent.jl
@@ -30,25 +30,24 @@ end
 _mo_output_covariance(k::IndependentMOKernel, out_dim) = Eye{Bool}(out_dim)
 
 function kernelmatrix(
-    k::IndependentMOKernel, x::IsotopicMOInputsUnion, y::IsotopicMOInputsUnion
-)
-    @assert x.out_dim == y.out_dim
+    k::IndependentMOKernel, x::MOI, y::MOI
+) where {MOI<:IsotopicMOInputsUnion}
+    x.out_dim == y.out_dim ||
+        throw(DimensionMismatch("`x` and `y` must have the same `out_dim`"))
     Kfeatures = kernelmatrix(k.kernel, x.x, y.x)
     Koutputs = _mo_output_covariance(k, x.out_dim)
-    return _kernelmatrix_kron_helper(x, Kfeatures, Koutputs)
+    return _kernelmatrix_kron_helper(MOI, Kfeatures, Koutputs)
 end
 
 if VERSION >= v"1.6"
     function kernelmatrix!(
-        K::AbstractMatrix,
-        k::IndependentMOKernel,
-        x::IsotopicMOInputsUnion,
-        y::IsotopicMOInputsUnion,
-    )
-        @assert x.out_dim == y.out_dim
+        K::AbstractMatrix, k::IndependentMOKernel, x::MOI, y::MOI
+    ) where {MOI<:IsotopicMOInputsUnion}
+        x.out_dim == y.out_dim ||
+            throw(DimensionMismatch("`x` and `y` must have the same `out_dim`"))
         Kfeatures = kernelmatrix(k.kernel, x.x, y.x)
         Koutputs = _mo_output_covariance(k, x.out_dim)
-        return _kernelmatrix_kron_helper!(K, x, Kfeatures, Koutputs)
+        return _kernelmatrix_kron_helper!(K, MOI, Kfeatures, Koutputs)
     end
 end
 
diff --git a/src/mokernels/intrinsiccoregion.jl b/src/mokernels/intrinsiccoregion.jl
index 7e5b884cd..0a940796b 100644
--- a/src/mokernels/intrinsiccoregion.jl
+++ b/src/mokernels/intrinsiccoregion.jl
@@ -48,25 +48,24 @@ function _mo_output_covariance(k::IntrinsicCoregionMOKernel, out_dim)
 end
 
 function kernelmatrix(
-    k::IntrinsicCoregionMOKernel, x::IsotopicMOInputsUnion, y::IsotopicMOInputsUnion
-)
-    @assert x.out_dim == y.out_dim
+    k::IntrinsicCoregionMOKernel, x::MOI, y::MOI
+) where {MOI<:IsotopicMOInputsUnion}
+    x.out_dim == y.out_dim ||
+        throw(DimensionMismatch("`x` and `y` must have the same `out_dim`"))
     Kfeatures = kernelmatrix(k.kernel, x.x, y.x)
     Koutputs = _mo_output_covariance(k, x.out_dim)
-    return _kernelmatrix_kron_helper(x, Kfeatures, Koutputs)
+    return _kernelmatrix_kron_helper(MOI, Kfeatures, Koutputs)
 end
 
 if VERSION >= v"1.6"
     function kernelmatrix!(
-        K::AbstractMatrix,
-        k::IntrinsicCoregionMOKernel,
-        x::IsotopicMOInputsUnion,
-        y::IsotopicMOInputsUnion,
-    )
-        @assert x.out_dim == y.out_dim
+        K::AbstractMatrix, k::IntrinsicCoregionMOKernel, x::MOI, y::MOI
+    ) where {MOI<:IsotopicMOInputsUnion}
+        x.out_dim == y.out_dim ||
+            throw(DimensionMismatch("`x` and `y` must have the same `out_dim`"))
         Kfeatures = kernelmatrix(k.kernel, x.x, y.x)
         Koutputs = _mo_output_covariance(k, x.out_dim)
-        return _kernelmatrix_kron_helper!(K, x, Kfeatures, Koutputs)
+        return _kernelmatrix_kron_helper!(K, MOI, Kfeatures, Koutputs)
     end
 end
 
diff --git a/src/mokernels/mokernel.jl b/src/mokernels/mokernel.jl
index acf0b78d5..30b6c2d9b 100644
--- a/src/mokernels/mokernel.jl
+++ b/src/mokernels/mokernel.jl
@@ -5,20 +5,24 @@ Abstract type for kernels with multiple outpus.
 """
 abstract type MOKernel <: Kernel end
 
-function _kernelmatrix_kron_helper(::MOInputIsotopicByFeatures, Kfeatures, Koutputs)
+function _kernelmatrix_kron_helper(::Type{<:MOInputIsotopicByFeatures}, Kfeatures, Koutputs)
     return kron(Kfeatures, Koutputs)
 end
 
-function _kernelmatrix_kron_helper(::MOInputIsotopicByOutputs, Kfeatures, Koutputs)
+function _kernelmatrix_kron_helper(::Type{<:MOInputIsotopicByOutputs}, Kfeatures, Koutputs)
     return kron(Koutputs, Kfeatures)
 end
 
 if VERSION >= v"1.6"
-    function _kernelmatrix_kron_helper!(K, ::MOInputIsotopicByFeatures, Kfeatures, Koutputs)
+    function _kernelmatrix_kron_helper!(
+        K, ::Type{<:MOInputIsotopicByFeatures}, Kfeatures, Koutputs
+    )
         return kron!(K, Kfeatures, Koutputs)
     end
 
-    function _kernelmatrix_kron_helper!(K, ::MOInputIsotopicByOutputs, Kfeatures, Koutputs)
+    function _kernelmatrix_kron_helper!(
+        K, ::Type{<:MOInputIsotopicByOutputs}, Kfeatures, Koutputs
+    )
         return kron!(K, Koutputs, Kfeatures)
     end
 end