diff --git a/src/Hecke.jl b/src/Hecke.jl
index 4e82997c2b..d5de31fd7e 100644
--- a/src/Hecke.jl
+++ b/src/Hecke.jl
@@ -556,6 +556,8 @@ order_type(T::DataType) = throw(MethodError(order_type, (T,)))
 embedding_type(x) = embedding_type(typeof(x))
 embedding_type(T::DataType) = throw(MethodError(embedding_type, (T,)))
 
+base_field_type(x) = base_field_type(typeof(x))
+base_field_type(T::DataType) = throw(MethodError(base_field_type, (T,)))
 
 ################################################################################
 #
diff --git a/src/LocalField/LocalField.jl b/src/LocalField/LocalField.jl
index 20ccf69de5..335626b38a 100644
--- a/src/LocalField/LocalField.jl
+++ b/src/LocalField/LocalField.jl
@@ -37,14 +37,10 @@ prime(K::LocalField) = prime(base_field(K))
 #
 ################################################################################
 
-base_field_type(K::LocalField{S, T}) where {S <: FieldElem, T <: LocalFieldParameter} = parent_type(S)
 base_field_type(::Type{LocalField{S, T}}) where {S <: FieldElem, T <: LocalFieldParameter} = parent_type(S)
 
 elem_type(::Type{LocalField{S, T}}) where {S <: FieldElem, T <: LocalFieldParameter} = LocalFieldElem{S, T}
 
-dense_poly_type(K::LocalField{S, T}) where {S <: FieldElem, T <: LocalFieldParameter} = Generic.Poly{LocalFieldElem{S, T}}
-dense_poly_type(::Type{LocalField{S, T}}) where {S <: FieldElem, T <: LocalFieldParameter} = Generic.Poly{LocalFieldElem{S, T}}
-
 ################################################################################
 #
 #  Basic predicates
diff --git a/src/Map/NumField.jl b/src/Map/NumField.jl
index 24275814cb..64848a6a80 100644
--- a/src/Map/NumField.jl
+++ b/src/Map/NumField.jl
@@ -182,13 +182,9 @@ end
 #
 ################################################################################
 
-base_field_type(::AbsSimpleNumField) = QQField
+base_field_type(::Type{AbsSimpleNumField}) = QQField
 
-base_field_type(::AbsNonSimpleNumField) = QQField
-
-base_field_type(::RelSimpleNumField{T}) where {T} = parent_type(T)
-
-base_field_type(::RelNonSimpleNumField{T}) where {T} = parent_type(T)
+base_field_type(::Type{AbsNonSimpleNumField}) = QQField
 
 base_field_type(::Type{RelNonSimpleNumField{T}}) where {T} = parent_type(T)
 
diff --git a/src/Misc/RelFiniteField.jl b/src/Misc/RelFiniteField.jl
index 2c030a6177..3d5eee6d01 100644
--- a/src/Misc/RelFiniteField.jl
+++ b/src/Misc/RelFiniteField.jl
@@ -56,6 +56,8 @@ function defining_polynomial(F::RelFinField{T}) where T
   return F.defining_polynomial::dense_poly_type(T)
 end
 
+base_field_type(::Type{RelFinField{S}}) where S = parent_type(S)
+
 base_field(F::RelFinField{S}) where S= base_ring(F.defining_polynomial)::parent_type(S)
 
 characteristic(F::RelFinField) = characteristic(base_field(F))