diff --git a/Project.toml b/Project.toml
index ef8435a0e..9ac9ac813 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "KernelFunctions"
 uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
-version = "0.10.53"
+version = "0.10.54"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
@@ -35,4 +35,4 @@ SpecialFunctions = "0.8, 0.9, 0.10, 1, 2"
 StatsBase = "0.32, 0.33"
 TensorCore = "0.1"
 ZygoteRules = "0.2"
-julia = "1.3"
+julia = "1.6"
diff --git a/src/basekernels/constant.jl b/src/basekernels/constant.jl
index e3f5245fb..cfbd8abc6 100644
--- a/src/basekernels/constant.jl
+++ b/src/basekernels/constant.jl
@@ -98,8 +98,8 @@ See also: [`ZeroKernel`](@ref)
 struct ConstantKernel{Tc<:Real} <: SimpleKernel
     c::Vector{Tc}
 
-    function ConstantKernel(; c::Real=1.0)
-        @check_args(ConstantKernel, c, c >= zero(c), "c ≥ 0")
+    function ConstantKernel(; c::Real=1.0, check_args::Bool=true)
+        @check_args(ConstantKernel, (c, c >= zero(c), "c ≥ 0"))
         return new{typeof(c)}([c])
     end
 end
diff --git a/src/basekernels/exponential.jl b/src/basekernels/exponential.jl
index 2061d40f9..0fc4b313f 100644
--- a/src/basekernels/exponential.jl
+++ b/src/basekernels/exponential.jl
@@ -125,14 +125,16 @@ struct GammaExponentialKernel{Tγ<:Real,M} <: SimpleKernel
     γ::Vector{Tγ}
     metric::M
 
-    function GammaExponentialKernel(γ::Real, metric)
-        @check_args(GammaExponentialKernel, γ, zero(γ) < γ ≤ 2, "γ ∈ (0, 2]")
+    function GammaExponentialKernel(γ::Real, metric; check_args::Bool=true)
+        @check_args(GammaExponentialKernel, (γ, zero(γ) < γ ≤ 2, "γ ∈ (0, 2]"))
         return new{typeof(γ),typeof(metric)}([γ], metric)
     end
 end
 
-function GammaExponentialKernel(; gamma::Real=1.0, γ::Real=gamma, metric=Euclidean())
-    return GammaExponentialKernel(γ, metric)
+function GammaExponentialKernel(;
+    gamma::Real=1.0, γ::Real=gamma, metric=Euclidean(), check_args::Bool=true
+)
+    return GammaExponentialKernel(γ, metric; check_args)
 end
 
 @functor GammaExponentialKernel
diff --git a/src/basekernels/fbm.jl b/src/basekernels/fbm.jl
index 422400ac4..b93933a9a 100644
--- a/src/basekernels/fbm.jl
+++ b/src/basekernels/fbm.jl
@@ -14,13 +14,13 @@ k(x, x'; h) =  \\frac{\\|x\\|_2^{2h} + \\|x'\\|_2^{2h} - \\|x - x'\\|^{2h}}{2}.
 """
 struct FBMKernel{T<:Real} <: Kernel
     h::Vector{T}
-    function FBMKernel(h::Real)
-        @check_args(FBMKernel, h, zero(h) ≤ h ≤ one(h), "h ∈ [0, 1]")
+    function FBMKernel(h::Real; check_args::Bool=true)
+        @check_args(FBMKernel, (h, zero(h) ≤ h ≤ one(h), "h ∈ [0, 1]"))
         return new{typeof(h)}([h])
     end
 end
 
-FBMKernel(; h::Real=0.5) = FBMKernel(h)
+FBMKernel(; h::Real=0.5, check_args::Bool=true) = FBMKernel(h; check_args)
 
 @functor FBMKernel
 
diff --git a/src/basekernels/matern.jl b/src/basekernels/matern.jl
index cb051ee0f..e1e7b8486 100644
--- a/src/basekernels/matern.jl
+++ b/src/basekernels/matern.jl
@@ -27,13 +27,15 @@ struct MaternKernel{Tν<:Real,M} <: SimpleKernel
     ν::Vector{Tν}
     metric::M
 
-    function MaternKernel(ν::Real, metric)
-        @check_args(MaternKernel, ν, ν > zero(ν), "ν > 0")
+    function MaternKernel(ν::Real, metric; check_args::Bool=true)
+        @check_args(MaternKernel, (ν, ν > zero(ν), "ν > 0"))
         return new{typeof(ν),typeof(metric)}([ν], metric)
     end
 end
 
-MaternKernel(; nu::Real=1.5, ν::Real=nu, metric=Euclidean()) = MaternKernel(ν, metric)
+function MaternKernel(; nu::Real=1.5, ν::Real=nu, metric=Euclidean(), check_args::Bool=true)
+    return MaternKernel(ν, metric; check_args)
+end
 
 @functor MaternKernel
 
diff --git a/src/basekernels/periodic.jl b/src/basekernels/periodic.jl
index 2758d7f94..8729e9606 100644
--- a/src/basekernels/periodic.jl
+++ b/src/basekernels/periodic.jl
@@ -15,8 +15,10 @@ k(x, x'; r) = \\exp\\bigg(- \\frac{1}{2} \\sum_{i=1}^d \\bigg(\\frac{\\sin\\big(
 """
 struct PeriodicKernel{T} <: SimpleKernel
     r::Vector{T}
-    function PeriodicKernel(; r::AbstractVector{<:Real}=ones(Float64, 1))
-        @check_args(PeriodicKernel, r, all(ri > zero(ri) for ri in r), "r > 0")
+    function PeriodicKernel(;
+        r::AbstractVector{<:Real}=ones(Float64, 1), check_args::Bool=true
+    )
+        @check_args(PeriodicKernel, (r, all(ri > zero(ri) for ri in r), "r > 0"))
         return new{eltype(r)}(r)
     end
 end
@@ -28,7 +30,9 @@ PeriodicKernel(dims::Int) = PeriodicKernel(Float64, dims)
 
 Create a [`PeriodicKernel`](@ref) with parameter `r=ones(T, dims)`.
 """
-PeriodicKernel(T::DataType, dims::Int=1) = PeriodicKernel(; r=ones(T, dims))
+function PeriodicKernel(T::DataType, dims::Int=1)
+    return PeriodicKernel(; r=ones(T, dims), check_args=false)
+end
 
 @functor PeriodicKernel
 
diff --git a/src/basekernels/polynomial.jl b/src/basekernels/polynomial.jl
index 0dbd2d52b..f2385efa5 100644
--- a/src/basekernels/polynomial.jl
+++ b/src/basekernels/polynomial.jl
@@ -16,13 +16,13 @@ See also: [`PolynomialKernel`](@ref)
 struct LinearKernel{Tc<:Real} <: SimpleKernel
     c::Vector{Tc}
 
-    function LinearKernel(c::Real)
-        @check_args(LinearKernel, c, c >= zero(c), "c ≥ 0")
+    function LinearKernel(c::Real; check_args::Bool=true)
+        @check_args(LinearKernel, (c, c >= zero(c), "c ≥ 0"))
         return new{typeof(c)}([c])
     end
 end
 
-LinearKernel(; c::Real=0.0) = LinearKernel(c)
+LinearKernel(; c::Real=0.0, check_args::Bool=true) = LinearKernel(c; check_args)
 
 @functor LinearKernel
 
@@ -69,15 +69,20 @@ struct PolynomialKernel{Tc<:Real} <: SimpleKernel
     degree::Int
     c::Vector{Tc}
 
-    function PolynomialKernel{Tc}(degree::Int, c::Vector{Tc}) where {Tc}
-        @check_args(PolynomialKernel, degree, degree >= one(degree), "degree ≥ 1")
-        @check_args(PolynomialKernel, c, only(c) >= zero(Tc), "c ≥ 0")
+    function PolynomialKernel{Tc}(
+        degree::Int, c::Vector{Tc}; check_args::Bool=true
+    ) where {Tc}
+        @check_args(
+            PolynomialKernel,
+            (degree, degree >= one(degree), "degree ≥ 1"),
+            (c, only(c) >= zero(Tc), "c ≥ 0")
+        )
         return new{Tc}(degree, c)
     end
 end
 
-function PolynomialKernel(; degree::Int=2, c::Real=0.0)
-    return PolynomialKernel{typeof(c)}(degree, [c])
+function PolynomialKernel(; degree::Int=2, c::Real=0.0, check_args::Bool=true)
+    return PolynomialKernel{typeof(c)}(degree, [c]; check_args)
 end
 
 # The degree of the polynomial kernel is a fixed discrete parameter
diff --git a/src/basekernels/rational.jl b/src/basekernels/rational.jl
index 835fe92ff..4ba0db22d 100644
--- a/src/basekernels/rational.jl
+++ b/src/basekernels/rational.jl
@@ -19,14 +19,16 @@ struct RationalKernel{Tα<:Real,M} <: SimpleKernel
     α::Vector{Tα}
     metric::M
 
-    function RationalKernel(α::Real, metric)
-        @check_args(RationalKernel, α, α > zero(α), "α > 0")
+    function RationalKernel(α::Real, metric; check_args::Bool=true)
+        @check_args(RationalKernel, (α, α > zero(α), "α > 0"))
         return new{typeof(α),typeof(metric)}([α], metric)
     end
 end
 
-function RationalKernel(; alpha::Real=2.0, α::Real=alpha, metric=Euclidean())
-    return RationalKernel(α, metric)
+function RationalKernel(;
+    alpha::Real=2.0, α::Real=alpha, metric=Euclidean(), check_args::Bool=true
+)
+    return RationalKernel(α, metric; check_args)
 end
 
 @functor RationalKernel
@@ -83,8 +85,10 @@ struct RationalQuadraticKernel{Tα<:Real,M} <: SimpleKernel
     α::Vector{Tα}
     metric::M
 
-    function RationalQuadraticKernel(; alpha::Real=2.0, α::Real=alpha, metric=Euclidean())
-        @check_args(RationalQuadraticKernel, α, α > zero(α), "α > 0")
+    function RationalQuadraticKernel(;
+        alpha::Real=2.0, α::Real=alpha, metric=Euclidean(), check_args::Bool=true
+    )
+        @check_args(RationalQuadraticKernel, (α, α > zero(α), "α > 0"))
         return new{typeof(α),typeof(metric)}([α], metric)
     end
 end
@@ -172,10 +176,18 @@ struct GammaRationalKernel{Tα<:Real,Tγ<:Real,M} <: SimpleKernel
     metric::M
 
     function GammaRationalKernel(;
-        alpha::Real=2.0, gamma::Real=1.0, α::Real=alpha, γ::Real=gamma, metric=Euclidean()
+        alpha::Real=2.0,
+        gamma::Real=1.0,
+        α::Real=alpha,
+        γ::Real=gamma,
+        metric=Euclidean(),
+        check_args::Bool=true,
     )
-        @check_args(GammaRationalKernel, α, α > zero(α), "α > 0")
-        @check_args(GammaRationalKernel, γ, zero(γ) < γ ≤ 2, "γ ∈ (0, 2]")
+        @check_args(
+            GammaRationalKernel,
+            (α, α > zero(α), "α > 0"),
+            (γ, zero(γ) < γ ≤ 2, "γ ∈ (0, 2]")
+        )
         return new{typeof(α),typeof(γ),typeof(metric)}([α], [γ], metric)
     end
 end
diff --git a/src/basekernels/wiener.jl b/src/basekernels/wiener.jl
index 14d330850..980b243ab 100644
--- a/src/basekernels/wiener.jl
+++ b/src/basekernels/wiener.jl
@@ -39,8 +39,8 @@ The [`WhiteKernel`](@ref) is recovered for ``i = -1``.
 [^SDH]: Schober, Duvenaud & Hennig (2014). Probabilistic ODE Solvers with Runge-Kutta Means.
 """
 struct WienerKernel{I} <: Kernel
-    function WienerKernel{I}() where {I}
-        @check_args(WienerKernel, I, I ∈ (-1, 0, 1, 2, 3), "I ∈ {-1, 0, 1, 2, 3}")
+    function WienerKernel{I}(; check_args::Bool=true) where {I}
+        @check_args(WienerKernel, (I, I ∈ (-1, 0, 1, 2, 3), "I ∈ {-1, 0, 1, 2, 3}"))
         if I == -1
             return WhiteKernel()
         end
diff --git a/src/kernels/scaledkernel.jl b/src/kernels/scaledkernel.jl
index 0a17943ac..6b20c6588 100644
--- a/src/kernels/scaledkernel.jl
+++ b/src/kernels/scaledkernel.jl
@@ -16,8 +16,10 @@ struct ScaledKernel{Tk<:Kernel,Tσ²<:Real} <: Kernel
     σ²::Vector{Tσ²}
 end
 
-function ScaledKernel(kernel::Tk, σ²::Tσ²=1.0) where {Tk<:Kernel,Tσ²<:Real}
-    @check_args(ScaledKernel, σ², σ² > zero(Tσ²), "σ² > 0")
+function ScaledKernel(
+    kernel::Tk, σ²::Tσ²=1.0; check_args::Bool=true
+) where {Tk<:Kernel,Tσ²<:Real}
+    @check_args(ScaledKernel, (σ², σ² > zero(Tσ²), "σ² > 0"))
     return ScaledKernel{Tk,Tσ²}(kernel, [σ²])
 end
 
diff --git a/src/mokernels/independent.jl b/src/mokernels/independent.jl
index 1f7811b14..554fdb08f 100644
--- a/src/mokernels/independent.jl
+++ b/src/mokernels/independent.jl
@@ -39,16 +39,14 @@ function kernelmatrix(
     return _kernelmatrix_kron_helper(MOI, Kfeatures, Koutputs)
 end
 
-if VERSION >= v"1.6"
-    function kernelmatrix!(
-        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, MOI, Kfeatures, Koutputs)
-    end
+function kernelmatrix!(
+    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, MOI, Kfeatures, Koutputs)
 end
 
 function Base.show(io::IO, k::IndependentMOKernel)
diff --git a/src/mokernels/intrinsiccoregion.jl b/src/mokernels/intrinsiccoregion.jl
index 0a940796b..cfa1118f0 100644
--- a/src/mokernels/intrinsiccoregion.jl
+++ b/src/mokernels/intrinsiccoregion.jl
@@ -19,23 +19,25 @@ struct IntrinsicCoregionMOKernel{K<:Kernel,T<:AbstractMatrix} <: MOKernel
     kernel::K
     B::T
 
-    function IntrinsicCoregionMOKernel{K,T}(kernel::K, B::T) where {K,T}
+    function IntrinsicCoregionMOKernel{K,T}(
+        kernel::K, B::T; check_args::Bool=true
+    ) where {K,T}
         @check_args(
             IntrinsicCoregionMOKernel,
-            B,
-            eigmin(B) >= 0,
-            "B has to be positive semi-definite"
+            (B, eigmin(B) >= 0, "B has to be positive semi-definite")
         )
         return new{K,T}(kernel, B)
     end
 end
 
-function IntrinsicCoregionMOKernel(; kernel::Kernel, B::AbstractMatrix)
-    return IntrinsicCoregionMOKernel{typeof(kernel),typeof(B)}(kernel, B)
+function IntrinsicCoregionMOKernel(;
+    kernel::Kernel, B::AbstractMatrix, check_args::Bool=true
+)
+    return IntrinsicCoregionMOKernel{typeof(kernel),typeof(B)}(kernel, B; check_args)
 end
 
-function IntrinsicCoregionMOKernel(kernel::Kernel, B::AbstractMatrix)
-    return IntrinsicCoregionMOKernel{typeof(kernel),typeof(B)}(kernel, B)
+function IntrinsicCoregionMOKernel(kernel::Kernel, B::AbstractMatrix; check_args::Bool=true)
+    return IntrinsicCoregionMOKernel{typeof(kernel),typeof(B)}(kernel, B; check_args)
 end
 
 function (k::IntrinsicCoregionMOKernel)((x, px)::Tuple{Any,Int}, (y, py)::Tuple{Any,Int})
@@ -57,16 +59,14 @@ function kernelmatrix(
     return _kernelmatrix_kron_helper(MOI, Kfeatures, Koutputs)
 end
 
-if VERSION >= v"1.6"
-    function kernelmatrix!(
-        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, MOI, Kfeatures, Koutputs)
-    end
+function kernelmatrix!(
+    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, MOI, Kfeatures, Koutputs)
 end
 
 function Base.show(io::IO, k::IntrinsicCoregionMOKernel)
diff --git a/src/mokernels/mokernel.jl b/src/mokernels/mokernel.jl
index 30b6c2d9b..474e193ea 100644
--- a/src/mokernels/mokernel.jl
+++ b/src/mokernels/mokernel.jl
@@ -13,16 +13,14 @@ function _kernelmatrix_kron_helper(::Type{<:MOInputIsotopicByOutputs}, Kfeatures
     return kron(Koutputs, Kfeatures)
 end
 
-if VERSION >= v"1.6"
-    function _kernelmatrix_kron_helper!(
-        K, ::Type{<:MOInputIsotopicByFeatures}, Kfeatures, Koutputs
-    )
-        return kron!(K, Kfeatures, Koutputs)
-    end
+function _kernelmatrix_kron_helper!(
+    K, ::Type{<:MOInputIsotopicByFeatures}, Kfeatures, Koutputs
+)
+    return kron!(K, Kfeatures, Koutputs)
+end
 
-    function _kernelmatrix_kron_helper!(
-        K, ::Type{<:MOInputIsotopicByOutputs}, Kfeatures, Koutputs
-    )
-        return kron!(K, Koutputs, Kfeatures)
-    end
+function _kernelmatrix_kron_helper!(
+    K, ::Type{<:MOInputIsotopicByOutputs}, Kfeatures, Koutputs
+)
+    return kron!(K, Koutputs, Kfeatures)
 end
diff --git a/src/utils.jl b/src/utils.jl
index bb805b15f..7d01f668f 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -1,24 +1,94 @@
-# Macro for checking arguments
-macro check_args(K, param, cond, desc=string(cond))
-    quote
-        if !($(esc(cond)))
-            throw(
-                ArgumentError(
-                    string(
-                        $(string(K)),
-                        ": ",
-                        $(string(param)),
-                        " = ",
-                        $(esc(param)),
-                        " does not ",
-                        "satisfy the constraint ",
-                        $(string(desc)),
-                        ".",
-                    ),
-                ),
-            )
+# strip_linenos and check_args both come from Distributions.jl,
+# see https://github.com/JuliaStats/Distributions.jl/blob/master/src/utils.jl
+
+macro strip_linenos(expr)
+    return esc(Base.remove_linenums!(expr))
+end
+
+"""
+    @check_args(
+        K,
+        @setup(statements...),
+        (arg₁, cond₁, message₁),
+        (cond₂, message₂),
+        ...,
+    )
+
+A convenience macro that generates checks of arguments for a kernel of type `K`.
+
+The macro expects that a boolean variable of name `check_args` is defined and generates
+the following Julia code:
+```julia
+KernelFunctions.check_args(check_args) do
+    \$(statements...)
+    cond₁ || throw(DomainError(arg₁, \$(string(D, ": ", message₁))))
+    cond₂ || throw(ArgumentError(\$(string(D, ": ", message₂))))
+    ...
+end
+```
+
+The `@setup` argument can be elided if no setup code is needed. Moreover, error messages
+can be omitted. In this case the message `"the condition \$(cond) is not satisfied."` is
+used.
+"""
+macro check_args(D, setup_or_check, checks...)
+    # Extract setup statements
+    if Meta.isexpr(setup_or_check, :macrocall) && setup_or_check.args[1] == Symbol("@setup")
+        setup_stmts = Any[esc(ex) for ex in setup_or_check.args[3:end]]
+    else
+        setup_stmts = []
+        checks = (setup_or_check, checks...)
+    end
+
+    # Generate expressions for each condition
+    conds_exprs = map(checks) do check
+        if Meta.isexpr(check, :tuple, 3)
+            # argument, condition, and message specified
+            arg = check.args[1]
+            cond = check.args[2]
+            message = string(D, ": ", check.args[3])
+            return :(($(esc(cond))) || throw(DomainError($(esc(arg)), $message)))
+        elseif Meta.isexpr(check, :tuple, 2)
+            cond_or_message = check.args[2]
+            if cond_or_message isa String
+                # only condition and message specified
+                cond = check.args[1]
+                message = string(D, ": ", cond_or_message)
+                return :(($(esc(cond))) || throw(ArgumentError($message)))
+            else
+                # only argument and condition specified
+                arg = check.args[1]
+                cond = cond_or_message
+                message = string(D, ": the condition ", cond, " is not satisfied.")
+                return :(($(esc(cond))) || throw(DomainError($(esc(arg)), $message)))
+            end
+        else
+            # only condition specified
+            cond = check
+            message = string(D, ": the condition ", cond, " is not satisfied.")
+            return :(($(esc(cond))) || throw(ArgumentError($message)))
         end
     end
+
+    return @strip_linenos quote
+        KernelFunctions.check_args($(esc(:check_args))) do
+            $(__source__)
+            $(setup_stmts...)
+            $(conds_exprs...)
+        end
+    end
+end
+
+"""
+    check_args(f, check::Bool)
+
+Perform check of arguments by calling a function `f`.
+
+If `check` is `false`, the checks are skipped.
+"""
+function check_args(f::F, check::Bool) where {F}
+    check && f()
+    return nothing
 end
 
 function deprecated_obsdim(obsdim::Union{Int,Nothing})
diff --git a/test/basekernels/polynomial.jl b/test/basekernels/polynomial.jl
index 80a3b1bb8..4c9104288 100644
--- a/test/basekernels/polynomial.jl
+++ b/test/basekernels/polynomial.jl
@@ -14,7 +14,7 @@
         @test repr(k) == "Linear Kernel (c = 0.0)"
 
         # Errors.
-        @test_throws ArgumentError LinearKernel(; c=-0.5)
+        @test_throws DomainError LinearKernel(; c=-0.5)
 
         # Standardised tests.
         TestUtils.test_interface(k, Float64)
@@ -36,8 +36,8 @@
         @test metric(PolynomialKernel(; degree=3, c=c)) == KernelFunctions.DotProduct()
 
         # Errors.
-        @test_throws ArgumentError PolynomialKernel(; degree=0)
-        @test_throws ArgumentError PolynomialKernel(; c=-0.5)
+        @test_throws DomainError PolynomialKernel(; degree=0)
+        @test_throws DomainError PolynomialKernel(; c=-0.5)
 
         # Standardised tests.
         TestUtils.test_interface(k, Float64)
diff --git a/test/basekernels/wiener.jl b/test/basekernels/wiener.jl
index 9dd60ba43..6d8c16c9a 100644
--- a/test/basekernels/wiener.jl
+++ b/test/basekernels/wiener.jl
@@ -14,8 +14,8 @@
     k3 = WienerKernel(; i=3)
     @test k3 isa WienerKernel{3}
 
-    @test_throws ArgumentError WienerKernel(; i=4)
-    @test_throws ArgumentError WienerKernel(; i=-2)
+    @test_throws DomainError WienerKernel(; i=4)
+    @test_throws DomainError WienerKernel(; i=-2)
 
     v1 = rand(4)
     v2 = rand(4)
diff --git a/test/chainrules.jl b/test/chainrules.jl
index 03c2c3b1f..4edd532d0 100644
--- a/test/chainrules.jl
+++ b/test/chainrules.jl
@@ -21,11 +21,7 @@
     compare_gradient(:Zygote, [x, y]) do xy
         KernelFunctions.Sinus(r)(xy[1], xy[2])
     end
-    if VERSION < v"1.6"
-        @test_broken "Chain rule of SqMahalanobis is broken in Julia pre-1.6"
-    else
-        compare_gradient(:Zygote, [Q, x, y]) do Qxy
-            SqMahalanobis(Qxy[1])(Qxy[2], Qxy[3])
-        end
+    compare_gradient(:Zygote, [Q, x, y]) do Qxy
+        SqMahalanobis(Qxy[1])(Qxy[2], Qxy[3])
     end
 end