diff --git a/src/flint/FlintTypes.jl b/src/flint/FlintTypes.jl
index eed807b56..d9b03b320 100644
--- a/src/flint/FlintTypes.jl
+++ b/src/flint/FlintTypes.jl
@@ -1363,7 +1363,7 @@ mutable struct ZZMPolyRingElem <: MPolyRingElem{ZZRingElem}
     return z
   end
 
-  ZZMPolyRingElem(ctx::ZZMPolyRing, a::Integer) = ZZMPolyRingElem(ctx, FlintInt(a))
+  ZZMPolyRingElem(ctx::ZZMPolyRing, a::Integer) = ZZMPolyRingElem(ctx, flintify(a))
 end
 
 function _fmpz_mpoly_clear_fn(a::ZZMPolyRingElem)
@@ -6472,20 +6472,21 @@ of methods that accept both Julia and Nemo integers or rationals.
 const RationalUnion = Union{Integer, ZZRingElem, Rational, QQFieldElem}
 
 """
-    FlintInt = Union{Int, ZZRingElem}
+    flintify(x::RationalUnion)
 
-The `FlintInt` type union is an internal helper for cleanly and compactly
-implementing efficient dispatch for arithmetics that involve native Nemo
-objects plus a Julia integer.
+Return either an `Int`, `ZZRingElem` or `QQFieldElem` equal to `x`.
 
-Many internal arithmetics functions in FLINT have optimize variants for
-the case when one operand is an `ZZRingElem` or an `Int` (sometimes also
-`UInt` is supported). E.g. there are special methods for adding
-one of these to a `ZZRingPolyElem`.
+This internal helper allow us to cleanly and compactly implement efficient
+dispatch for arithmetics that involve native Nemo objects plus a Julia
+integer.
 
-In order to handling adding an arbitrary Julia integer to a
-`ZZRingPolyElem`, further dispatch is needed. The easiest is to
-provide a method
+Indeed, many internal arithmetics functions in FLINT have optimize variants
+for the case when one operand is an `ZZRingElem` or an `Int` (sometimes also
+`UInt` is supported). E.g. there are special methods for adding one of these
+to a `ZZRingPolyElem`.
+
+In order to handling adding an arbitrary Julia integer to a `ZZRingPolyElem`,
+further dispatch is needed. The easiest is to provide a method
 
     +(a::ZZRingPolyElem, b::Integer) = a + ZZ(b)
 
@@ -6496,37 +6497,26 @@ do this (at least on a 64 bit machine):
     +(a::ZZRingPolyElem, b::{Int64,Int32,Int16,Int8,UInt32,UInt16,UInt8}) = a + Int(b)
 
 Doing this repeatedly is cumbersome and error prone. This can be avoided by
-using `FlintInt`, which allows us to write
+using `flintify`, which allows us to write
 
-    +(a::ZZRingPolyElem, b::Integer) = a + FlintInt(b)
+    +(a::ZZRingPolyElem, b::Integer) = a + flintify(b)
 
 to get optimal dispatch.
 
 This also works for Nemo types that also have special handlers for `UInt`,
 as their method for `b::UInt` takes precedence over the fallback method.
 """
-const FlintInt = Union{Int, ZZRingElem}
-
-FlintInt(x::ZZRingElem) = x
-FlintInt(x::Integer) = ZZRingElem(x)::ZZRingElem
+flintify(x::ZZRingElem) = x
+flintify(x::QQFieldElem) = x
+flintify(x::Int) = x
+flintify(x::Integer) = ZZRingElem(x)::ZZRingElem
+flintify(x::Rational) = QQFieldElem(x)::QQFieldElem
 @static if Int === Int64
-  FlintInt(x::Union{Int64,Int32,Int16,Int8,UInt32,UInt16,UInt8}) = Int(x)
+  flintify(x::Union{Int64,Int32,Int16,Int8,UInt32,UInt16,UInt8}) = Int(x)
 else
-  FlintInt(x::Union{Int32,Int16,Int8,UInt16,UInt8}) = Int(x)
+  flintify(x::Union{Int32,Int16,Int8,UInt16,UInt8}) = Int(x)
 end
 
-"""
-    FlintRat = Union{FlintInt, QQFieldElem}
-
-The `FlintRat` type union is an internal helper similar to [`FlintInt`](@ref)
-but also accepting `QQFieldElem` and `Rational{<:Integer}` arguments.
-"""
-const FlintRat = Union{FlintInt, QQFieldElem}
-
-FlintRat(x::QQFieldElem) = x
-FlintRat(x::Rational{<:Integer}) = QQFieldElem(x)::QQFieldElem
-FlintRat(x::Integer) = FlintInt(x)
-
 
 const ZmodNFmpzPolyRing = Union{ZZModPolyRing, FpPolyRing}
 
diff --git a/src/flint/fmpq_mpoly.jl b/src/flint/fmpq_mpoly.jl
index 726d66dbf..1e28cac7b 100644
--- a/src/flint/fmpq_mpoly.jl
+++ b/src/flint/fmpq_mpoly.jl
@@ -364,11 +364,11 @@ for (jT, cN, cT) in ((QQFieldElem, :fmpq, Ref{QQFieldElem}), (ZZRingElem, :fmpz,
   end
 end
 
-+(a::QQMPolyRingElem, b::Integer) = a + FlintInt(b)
++(a::QQMPolyRingElem, b::Integer) = a + flintify(b)
 
 +(a::Integer, b::QQMPolyRingElem) = b + a
 
--(a::QQMPolyRingElem, b::Integer) = a - FlintInt(b)
+-(a::QQMPolyRingElem, b::Integer) = a - flintify(b)
 
 -(a::Integer, b::QQMPolyRingElem) = neg!(b - a)
 
@@ -380,7 +380,7 @@ end
 
 -(a::Rational{<:Integer}, b::QQMPolyRingElem) = neg!(b - a)
 
-*(a::QQMPolyRingElem, b::Integer) = a * FlintInt(b)
+*(a::QQMPolyRingElem, b::Integer) = a * flintify(b)
 
 *(a::Integer, b::QQMPolyRingElem) = b * a
 
@@ -388,11 +388,11 @@ end
 
 *(a::Rational{<:Integer}, b::QQMPolyRingElem) = b * a
 
-divexact(a::QQMPolyRingElem, b::Integer; check::Bool=true) = divexact(a, FlintInt(b); check=check)
+divexact(a::QQMPolyRingElem, b::Integer; check::Bool=true) = divexact(a, flintify(b); check=check)
 
 divexact(a::QQMPolyRingElem, b::Rational{<:Integer}; check::Bool=true) = divexact(a, QQFieldElem(b); check=check)
 
-//(a::QQMPolyRingElem, b::Integer) = //(a, FlintInt(b))
+//(a::QQMPolyRingElem, b::Integer) = //(a, flintify(b))
 
 //(a::QQMPolyRingElem, b::Rational{<:Integer}) = //(a, QQFieldElem(b))
 
@@ -573,7 +573,7 @@ end
 
 ==(a::Int, b::QQMPolyRingElem) = b == a
 
-==(a::QQMPolyRingElem, b::Integer) = a == FlintInt(b)
+==(a::QQMPolyRingElem, b::Integer) = a == flintify(b)
 
 ==(a::Integer, b::QQMPolyRingElem) = b == a
 
@@ -1186,7 +1186,7 @@ function (R::QQMPolyRing)(b::RationalUnion)
   return z
 end
 
-QQMPolyRingElem(ctx::QQMPolyRing, a::RationalUnion) = QQMPolyRingElem(ctx, FlintRat(a))
+QQMPolyRingElem(ctx::QQMPolyRing, a::RationalUnion) = QQMPolyRingElem(ctx, flintify(a))
 
 function (R::QQMPolyRing)(a::QQMPolyRingElem)
   parent(a) != R && error("Unable to coerce polynomial")
diff --git a/src/flint/fmpz_poly.jl b/src/flint/fmpz_poly.jl
index 67e710e3e..c1ccf333e 100644
--- a/src/flint/fmpz_poly.jl
+++ b/src/flint/fmpz_poly.jl
@@ -225,17 +225,17 @@ end
 
 *(x::ZZPolyRingElem, y::ZZRingElem) = y*x
 
-+(x::Integer, y::ZZPolyRingElem) = y + FlintInt(x)
++(x::Integer, y::ZZPolyRingElem) = y + flintify(x)
 
--(x::Integer, y::ZZPolyRingElem) = FlintInt(x) - y
+-(x::Integer, y::ZZPolyRingElem) = flintify(x) - y
 
-*(x::Integer, y::ZZPolyRingElem) = FlintInt(x)*y
+*(x::Integer, y::ZZPolyRingElem) = flintify(x)*y
 
-+(x::ZZPolyRingElem, y::Integer) = x + FlintInt(y)
++(x::ZZPolyRingElem, y::Integer) = x + flintify(y)
 
--(x::ZZPolyRingElem, y::Integer) = x - FlintInt(y)
+-(x::ZZPolyRingElem, y::Integer) = x - flintify(y)
 
-*(x::ZZPolyRingElem, y::Integer) = FlintInt(y)*x
+*(x::ZZPolyRingElem, y::Integer) = flintify(y)*x
 
 ###############################################################################
 #
@@ -943,7 +943,7 @@ function (a::ZZPolyRing)()
 end
 
 function (a::ZZPolyRing)(b::IntegerUnion)
-  z = ZZPolyRingElem(FlintInt(b))
+  z = ZZPolyRingElem(flintify(b))
   z.parent = a
   return z
 end