diff --git a/src/arb/ArbTypes.jl b/src/arb/ArbTypes.jl
index 6a078ed14..47b23490d 100644
--- a/src/arb/ArbTypes.jl
+++ b/src/arb/ArbTypes.jl
@@ -467,16 +467,14 @@ mutable struct RealPolyRingElem <: PolyRingElem{RealFieldElem}
 
   function RealPolyRingElem(x::RealFieldElem, p::Int)
     z = RealPolyRingElem()
-    ccall((:arb_poly_set_coeff_arb, libflint), Nothing,
-          (Ref{RealPolyRingElem}, Int, Ref{RealFieldElem}), z, 0, x)
+    setcoeff!(z, 0, x)
     return z
   end
 
   function RealPolyRingElem(x::Vector{RealFieldElem}, p::Int)
     z = RealPolyRingElem()
-    for i = 1:length(x)
-      ccall((:arb_poly_set_coeff_arb, libflint), Nothing,
-            (Ref{RealPolyRingElem}, Int, Ref{RealFieldElem}), z, i - 1, x[i])
+    for i in 1:length(x)
+      setcoeff!(z, i - 1, x[i])
     end
     return z
   end
@@ -549,16 +547,14 @@ mutable struct ArbPolyRingElem <: PolyRingElem{ArbFieldElem}
 
   function ArbPolyRingElem(x::ArbFieldElem, p::Int)
     z = ArbPolyRingElem()
-    ccall((:arb_poly_set_coeff_arb, libflint), Nothing,
-          (Ref{ArbPolyRingElem}, Int, Ref{ArbFieldElem}), z, 0, x)
+    setcoeff!(z, 0, x)
     return z
   end
 
   function ArbPolyRingElem(x::Vector{ArbFieldElem}, p::Int)
     z = ArbPolyRingElem()
-    for i = 1:length(x)
-      ccall((:arb_poly_set_coeff_arb, libflint), Nothing,
-            (Ref{ArbPolyRingElem}, Int, Ref{ArbFieldElem}), z, i - 1, x[i])
+    for i in 1:length(x)
+      setcoeff!(z, i - 1, x[i])
     end
     return z
   end
@@ -636,16 +632,14 @@ mutable struct ComplexPolyRingElem <: PolyRingElem{ComplexFieldElem}
 
   function ComplexPolyRingElem(x::ComplexFieldElem, p::Int)
     z = ComplexPolyRingElem()
-    ccall((:acb_poly_set_coeff_acb, libflint), Nothing,
-          (Ref{ComplexPolyRingElem}, Int, Ref{ComplexFieldElem}), z, 0, x)
+    setcoeff!(z, 0, x)
     return z
   end
 
   function ComplexPolyRingElem(x::Vector{ComplexFieldElem}, p::Int)
     z = ComplexPolyRingElem()
-    for i = 1:length(x)
-      ccall((:acb_poly_set_coeff_acb, libflint), Nothing,
-            (Ref{ComplexPolyRingElem}, Int, Ref{ComplexFieldElem}), z, i - 1, x[i])
+    for i in 1:length(x)
+      setcoeff!(z, i - 1, x[i])
     end
     return z
   end
@@ -727,16 +721,14 @@ mutable struct AcbPolyRingElem <: PolyRingElem{AcbFieldElem}
 
   function AcbPolyRingElem(x::AcbFieldElem, p::Int)
     z = AcbPolyRingElem()
-    ccall((:acb_poly_set_coeff_acb, libflint), Nothing,
-          (Ref{AcbPolyRingElem}, Int, Ref{AcbFieldElem}), z, 0, x)
+    setcoeff!(z, 0, x)
     return z
   end
 
   function AcbPolyRingElem(x::Vector{AcbFieldElem}, p::Int)
     z = AcbPolyRingElem()
-    for i = 1:length(x)
-      ccall((:acb_poly_set_coeff_acb, libflint), Nothing,
-            (Ref{AcbPolyRingElem}, Int, Ref{AcbFieldElem}), z, i - 1, x[i])
+    for i in 1:length(x)
+      setcoeff!(z, i - 1, x[i])
     end
     return z
   end
diff --git a/src/arb/ComplexPoly.jl b/src/arb/ComplexPoly.jl
index 76071a8d9..b37cbebc5 100644
--- a/src/arb/ComplexPoly.jl
+++ b/src/arb/ComplexPoly.jl
@@ -41,8 +41,7 @@ one(a::ComplexPolyRing) = one!(a())
 
 function gen(a::ComplexPolyRing)
   z = ComplexPolyRingElem()
-  ccall((:acb_poly_set_coeff_si, libflint), Nothing,
-        (Ref{ComplexPolyRingElem}, Int, Int), z, 1, 1)
+  setcoeff!(z, 1, 1)
   z.parent = a
   return z
 end
@@ -705,18 +704,24 @@ function fit!(z::ComplexPolyRingElem, n::Int)
   return nothing
 end
 
-function setcoeff!(z::ComplexPolyRingElem, n::Int, x::ZZRingElem)
-  ccall((:acb_poly_set_coeff_fmpz, libflint), Nothing,
-        (Ref{ComplexPolyRingElem}, Int, Ref{ZZRingElem}), z, n, x)
-  return z
-end
-
 function setcoeff!(z::ComplexPolyRingElem, n::Int, x::ComplexFieldElem)
   ccall((:acb_poly_set_coeff_acb, libflint), Nothing,
         (Ref{ComplexPolyRingElem}, Int, Ref{ComplexFieldElem}), z, n, x)
   return z
 end
 
+function setcoeff!(z::ComplexPolyRingElem, n::Int, x::Int)
+  ccall((:acb_poly_set_coeff_si, libflint), Nothing,
+        (Ref{ComplexPolyRingElem}, Int, Int), z, n, x)
+  return z
+end
+
+function setcoeff!(z::ComplexPolyRingElem, n::Int, x::ZZRingElem)
+  return setcoeff!(z, n, base_ring(z)(x))
+end
+
+setcoeff!(z::ComplexPolyRingElem, n::Int, x::Integer) = setcoeff!(z, n, flintify(x))
+
 #
 
 function add!(z::ComplexPolyRingElem, x::ComplexPolyRingElem, y::ComplexPolyRingElem)
diff --git a/src/arb/RealPoly.jl b/src/arb/RealPoly.jl
index ff4cd9008..a2d5826b5 100644
--- a/src/arb/RealPoly.jl
+++ b/src/arb/RealPoly.jl
@@ -41,8 +41,7 @@ one(a::RealPolyRing) = one!(a())
 
 function gen(a::RealPolyRing)
   z = RealPolyRingElem()
-  ccall((:arb_poly_set_coeff_si, libflint), Nothing,
-        (Ref{RealPolyRingElem}, Int, Int), z, 1, 1)
+  setcoeff!(z, 1, 1)
   z.parent = a
   return z
 end
@@ -608,18 +607,24 @@ function fit!(z::RealPolyRingElem, n::Int)
   return nothing
 end
 
-function setcoeff!(z::RealPolyRingElem, n::Int, x::ZZRingElem)
-  ccall((:arb_poly_set_coeff_fmpz, libflint), Nothing,
-        (Ref{RealPolyRingElem}, Int, Ref{ZZRingElem}), z, n, x)
-  return z
-end
-
 function setcoeff!(z::RealPolyRingElem, n::Int, x::RealFieldElem)
   ccall((:arb_poly_set_coeff_arb, libflint), Nothing,
         (Ref{RealPolyRingElem}, Int, Ref{RealFieldElem}), z, n, x)
   return z
 end
 
+function setcoeff!(z::RealPolyRingElem, n::Int, x::Int)
+  ccall((:arb_poly_set_coeff_si, libflint), Nothing,
+        (Ref{RealPolyRingElem}, Int, Int), z, n, x)
+  return z
+end
+
+function setcoeff!(z::RealPolyRingElem, n::Int, x::ZZRingElem)
+  return setcoeff!(z, n, base_ring(z)(x))
+end
+
+setcoeff!(z::RealPolyRingElem, n::Int, x::Integer) = setcoeff!(z, n, flintify(x))
+
 #
 
 function add!(z::RealPolyRingElem, x::RealPolyRingElem, y::RealPolyRingElem)
diff --git a/src/arb/acb_poly.jl b/src/arb/acb_poly.jl
index e6c26f287..cdc6bac12 100644
--- a/src/arb/acb_poly.jl
+++ b/src/arb/acb_poly.jl
@@ -41,8 +41,7 @@ one(a::AcbPolyRing) = one!(a())
 
 function gen(a::AcbPolyRing)
   z = AcbPolyRingElem()
-  ccall((:acb_poly_set_coeff_si, libflint), Nothing,
-        (Ref{AcbPolyRingElem}, Int, Int), z, 1, 1)
+  setcoeff!(z, 1, 1)
   z.parent = a
   return z
 end
@@ -701,18 +700,24 @@ function fit!(z::AcbPolyRingElem, n::Int)
   return nothing
 end
 
-function setcoeff!(z::AcbPolyRingElem, n::Int, x::ZZRingElem)
-  ccall((:acb_poly_set_coeff_fmpz, libflint), Nothing,
-        (Ref{AcbPolyRingElem}, Int, Ref{ZZRingElem}), z, n, x)
-  return z
-end
-
 function setcoeff!(z::AcbPolyRingElem, n::Int, x::AcbFieldElem)
   ccall((:acb_poly_set_coeff_acb, libflint), Nothing,
         (Ref{AcbPolyRingElem}, Int, Ref{AcbFieldElem}), z, n, x)
   return z
 end
 
+function setcoeff!(z::AcbPolyRingElem, n::Int, x::Int)
+  ccall((:acb_poly_set_coeff_si, libflint), Nothing,
+        (Ref{AcbPolyRingElem}, Int, Int), z, n, x)
+  return z
+end
+
+function setcoeff!(z::AcbPolyRingElem, n::Int, x::ZZRingElem)
+  return setcoeff!(z, n, base_ring(z)(x))
+end
+
+setcoeff!(z::AcbPolyRingElem, n::Int, x::Integer) = setcoeff!(z, n, flintify(x))
+
 #
 
 function add!(z::AcbPolyRingElem, x::AcbPolyRingElem, y::AcbPolyRingElem)
diff --git a/src/arb/arb_poly.jl b/src/arb/arb_poly.jl
index 32744e189..2eb1156b3 100644
--- a/src/arb/arb_poly.jl
+++ b/src/arb/arb_poly.jl
@@ -41,8 +41,7 @@ one(a::ArbPolyRing) = one!(a())
 
 function gen(a::ArbPolyRing)
   z = ArbPolyRingElem()
-  ccall((:arb_poly_set_coeff_si, libflint), Nothing,
-        (Ref{ArbPolyRingElem}, Int, Int), z, 1, 1)
+  setcoeff!(z, 1, 1)
   z.parent = a
   return z
 end
@@ -608,18 +607,24 @@ function fit!(z::ArbPolyRingElem, n::Int)
   return nothing
 end
 
-function setcoeff!(z::ArbPolyRingElem, n::Int, x::ZZRingElem)
-  ccall((:arb_poly_set_coeff_fmpz, libflint), Nothing,
-        (Ref{ArbPolyRingElem}, Int, Ref{ZZRingElem}), z, n, x)
-  return z
-end
-
 function setcoeff!(z::ArbPolyRingElem, n::Int, x::ArbFieldElem)
   ccall((:arb_poly_set_coeff_arb, libflint), Nothing,
         (Ref{ArbPolyRingElem}, Int, Ref{ArbFieldElem}), z, n, x)
   return z
 end
 
+function setcoeff!(z::ArbPolyRingElem, n::Int, x::Int)
+  ccall((:arb_poly_set_coeff_si, libflint), Nothing,
+        (Ref{ArbPolyRingElem}, Int, Int), z, n, x)
+  return z
+end
+
+function setcoeff!(z::ArbPolyRingElem, n::Int, x::ZZRingElem)
+  return setcoeff!(z, n, base_ring(z)(x))
+end
+
+setcoeff!(z::ArbPolyRingElem, n::Int, x::Integer) = setcoeff!(z, n, flintify(x))
+
 #
 
 function add!(z::ArbPolyRingElem, x::ArbPolyRingElem, y::ArbPolyRingElem)