diff --git a/test/construction.jl b/test/construction.jl
index cf7786d..9ee0bd1 100644
--- a/test/construction.jl
+++ b/test/construction.jl
@@ -79,6 +79,21 @@ end
     @test CliffordNumbers.Z2CliffordNumber(k2) === EvenCliffordNumber{VGA(3)}(0, 1, 2, 3)
 end
 
+@testset "Abstract constructors" begin
+    k = KVector{1,VGA(3)}(4, 2, 0)
+    # Things that should work
+    @test AbstractCliffordNumber(k) === k
+    @test AbstractCliffordNumber{VGA(3)}(k) === k
+    @test AbstractCliffordNumber{VGA(3),scalar_type(k)}(k) === k
+    @test AbstractCliffordNumber{VGA(3),Float64}(k) === float(k)
+    @test AbstractCliffordNumber{VGA(3)}(1) === one(KVector{0,VGA(3),Int})
+    @test AbstractCliffordNumber{VGA(3),Float64}(1) === one(KVector{0,VGA(3),Float64})
+    # Things that shouldn't work
+    @test_throws ArgumentError AbstractCliffordNumber(1)
+    @test_throws ArgumentError AbstractCliffordNumber(MockNumber())
+    @test_throws ArgumentError AbstractCliffordNumber{VGA(3)}(MockNumber())
+end
+
 @testset "Similar types" begin
     import CliffordNumbers.similar_type
     @test similar_type(EvenCliffordNumber{VGA(3),Int}, Val(STA)) === EvenCliffordNumber{STA,Int,8}
diff --git a/test/conversion.jl b/test/conversion.jl
index fbc242d..afa1ba6 100644
--- a/test/conversion.jl
+++ b/test/conversion.jl
@@ -24,6 +24,21 @@
     @test scalar_convert(Float32, 2) === Float32(2)
 end
 
+@testset "Abstract conversion" begin
+    k = KVector{1,VGA(3)}(4, 2, 0)
+    # Things that should work
+    @test convert(AbstractCliffordNumber, k) === k
+    @test convert(AbstractCliffordNumber{VGA(3)}, k) === k
+    @test convert(AbstractCliffordNumber{VGA(3),scalar_type(k)}, k) === k
+    @test convert(AbstractCliffordNumber{VGA(3),Float64}, k) === float(k)
+    @test convert(AbstractCliffordNumber{VGA(3)}, 1) === one(KVector{0,VGA(3),Int})
+    @test convert(AbstractCliffordNumber{VGA(3),Float64}, 1) === one(KVector{0,VGA(3),Float64})
+    # Things that shouldn't
+    @test_throws ArgumentError convert(AbstractCliffordNumber, 1)
+    @test_throws ArgumentError convert(AbstractCliffordNumber, MockNumber())
+    @test_throws ArgumentError convert(AbstractCliffordNumber{VGA(3)}, MockNumber())
+end
+
 @testset "Promotion" begin
     @test promote_type(Int, CliffordNumber{VGA(3)}) === CliffordNumber{VGA(3)}
     @test promote_type(Int, CliffordNumber{VGA(3),Float64}) === CliffordNumber{VGA(3),Float64,8}
diff --git a/test/runtests.jl b/test/runtests.jl
index 1d0b014..1f0f0ca 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -9,6 +9,10 @@ Aqua.test_all(CliffordNumbers; unbound_args = false)
 @basis_vars(PGA(3), Int)
 @basis_vars(STA)
 
+# A subtype of Number that does not subtype Real or Complex
+struct MockNumber <: Number
+end
+
 @testset "CliffordNumbers.jl" begin
     include("internals.jl")
     include("metrics.jl")