diff --git a/Project.toml b/Project.toml
index ea93c247..e0344b23 100644
--- a/Project.toml
+++ b/Project.toml
@@ -2,7 +2,7 @@ name = "Polynomials"
 uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
 license = "MIT"
 author = "JuliaMath"
-version = "2.0.15"
+version = "2.0.16"
 
 [deps]
 Intervals = "d8418881-c3e1-53bb-8760-2df7ec849ed5"
diff --git a/src/abstract.jl b/src/abstract.jl
index a32c8ce4..1d6fbc69 100644
--- a/src/abstract.jl
+++ b/src/abstract.jl
@@ -92,6 +92,9 @@ macro register(name)
             cs = collect(coeffs)
             $poly{eltype(cs), Symbol(var)}(cs)
         end
+        $poly{T,X}(c::AbstractPolynomial{S,Y}) where {T,X,S,Y} = convert($poly{T,X}, c)
+        $poly{T}(c::AbstractPolynomial{S,Y}) where {T,S,Y} = convert($poly{T}, c)
+        $poly(c::AbstractPolynomial{S,Y}) where {S,Y} = convert($poly, c)
         $poly{T,X}(n::S) where {T, X, S<:Number} =
             T(n) *  one($poly{T, X})
         $poly{T}(n::S, var::SymbolLike = :x) where {T, S<:Number} =
@@ -121,6 +124,9 @@ macro registerN(name, params...)
         end
         $poly{$(αs...)}(coeffs::AbstractVector{T}, var::SymbolLike=:x) where {$(αs...),T} =
             $poly{$(αs...),T,Symbol(var)}(coeffs)
+        $poly{$(as...),T,X}(c::AbstractPolynomial{S,Y}) where {$(as...),T,X,S,Y} = convert($poly{$(as...),T,X}, c)
+        $poly{$(as...),T}(c::AbstractPolynomial{S,Y}) where {$(as...),T,S,Y} = convert($poly{$(as...),T}, c)
+        $poly{$(as...),}(c::AbstractPolynomial{S,Y}) where {$(as...),S,Y} = convert($poly{$(as...),}, c)
 
         $poly{$(αs...),T,X}(n::Number) where {$(αs...),T,X} = T(n)*one($poly{$(αs...),T,X})
         $poly{$(αs...),T}(n::Number, var::SymbolLike = :x) where {$(αs...),T} = T(n)*one($poly{$(αs...),T,Symbol(var)})
diff --git a/src/polynomials/ChebyshevT.jl b/src/polynomials/ChebyshevT.jl
index 37984259..d5c6d7d7 100644
--- a/src/polynomials/ChebyshevT.jl
+++ b/src/polynomials/ChebyshevT.jl
@@ -75,7 +75,12 @@ function Base.convert(P::Type{<:Polynomial}, ch::ChebyshevT)
     end
     return c0 + c1 * x
 end
-Base.convert(C::Type{<:ChebyshevT}, p::Polynomial) = p(variable(C))
+
+function Base.convert(C::Type{<:ChebyshevT}, p::Polynomial)
+    x = variable(C)
+    isconstant(p) || assert_same_variable(indeterminate(x),indeterminate(p))
+    p(x)
+end
 
 Base.promote_rule(::Type{P},::Type{Q}) where {T, X, P <: LaurentPolynomial{T,X}, S, Q <: ChebyshevT{S, X}} = LaurentPolynomial{promote_type(T, S), X}
 
diff --git a/test/StandardBasis.jl b/test/StandardBasis.jl
index e7d89972..6da5683a 100644
--- a/test/StandardBasis.jl
+++ b/test/StandardBasis.jl
@@ -736,6 +736,15 @@ end
     # issue #287
     p = LaurentPolynomial([1], -5)
     @test p ≈ convert(LaurentPolynomial{Float64}, p)
+
+    # issue #358 `P(p::AbstractPolynomial)` should be `convert(P, p)` not `P(pᵢ for pᵢ ∈ p))`
+    x² = Polynomial([0,0,1], :x)
+    for P ∈ (ImmutablePolynomial, SparsePolynomial, ChebyshevT)
+        @test P(x²) == convert(P, x²)
+        Q = P{Float64}
+        @test Q(x²) == convert(Q, x²)
+    end
+
 end
 
 @testset "Roots" begin