diff --git a/src/bases/fourier/fourier.jl b/src/bases/fourier/fourier.jl
index 421cd170..ce2048a3 100644
--- a/src/bases/fourier/fourier.jl
+++ b/src/bases/fourier/fourier.jl
@@ -25,7 +25,6 @@ name(b::Fourier) = "Fourier series"
 # The default numeric type is Float64
 Fourier(n::Int) = Fourier{Float64}(n)
 
-convert(::Type{Fourier{T}}, d::Fourier{T}) where {T} = d
 convert(::Type{Fourier{T}}, d::Fourier) where {T} = Fourier{T}(d.n)
 
 @deprecate Fourier(n, a::Number, b::Number) Fourier(n)→a..b
diff --git a/src/bases/poly/chebyshev/ChebyshevT.jl b/src/bases/poly/chebyshev/ChebyshevT.jl
index e46f4d3c..c0a5c086 100644
--- a/src/bases/poly/chebyshev/ChebyshevT.jl
+++ b/src/bases/poly/chebyshev/ChebyshevT.jl
@@ -14,6 +14,8 @@ ChebyshevT(n::Int) = ChebyshevT{Float64}(n)
 
 similar(b::ChebyshevT, ::Type{T}, n::Int) where {T} = ChebyshevT{T}(n)
 
+convert(::Type{ChebyshevT{T}}, d::ChebyshevT) where {T} = ChebyshevT{T}(d.n)
+
 "Mapped Chebyshev polynomials."
 struct MappedChebyshev{T} <: MappedDict{T,T}
 	superdict	::	ChebyshevT{T}
diff --git a/test/test_chebyshev.jl b/test/test_chebyshev.jl
index 5117d265..537fdb54 100644
--- a/test/test_chebyshev.jl
+++ b/test/test_chebyshev.jl
@@ -8,6 +8,7 @@ function test_chebyshev_expansions(T)
         g = BasisFunctions.secondgrid(b)
         BasisFunctions.Test.test_generic_dict_transform(b, g)
         BasisFunctions.Test.test_generic_dict_transform(complex(b), g)
+        @test convert(ChebyshevT{BigFloat}, ChebyshevT{T}(10)) isa ChebyshevT{BigFloat}
     end
 
     @test support(b) == ChebyshevInterval{T}()
diff --git a/test/test_fourier.jl b/test/test_fourier.jl
index c1af724d..78f2283c 100644
--- a/test/test_fourier.jl
+++ b/test/test_fourier.jl
@@ -17,6 +17,8 @@ function test_fourier_series(T)
 
     @test support(fb0) == UnitInterval{T}()
 
+    @test convert(Fourier{BigFloat}, Fourier{Float64}(10)) isa Fourier{BigFloat}
+
     ## Even length
     n = 12
     a = -T(1.2)