diff --git a/docs/src/submodules/Bridges/reference.md b/docs/src/submodules/Bridges/reference.md
index 753c60919f..25047bf95f 100644
--- a/docs/src/submodules/Bridges/reference.md
+++ b/docs/src/submodules/Bridges/reference.md
@@ -90,6 +90,7 @@ Bridges.debug_supports
 ## [SetMap API](@id constraint_set_map)
 
 ```@docs
+Bridges.MapNotInvertible
 Bridges.map_set
 Bridges.inverse_map_set
 Bridges.map_function
diff --git a/src/Bridges/Constraint/set_map.jl b/src/Bridges/Constraint/set_map.jl
index d6eb9cc82d..97dd605adb 100644
--- a/src/Bridges/Constraint/set_map.jl
+++ b/src/Bridges/Constraint/set_map.jl
@@ -105,11 +105,13 @@ function MOI.get(
     func = try
         MOI.Bridges.inverse_map_function(bridge, mapped_func)
     catch err
+        # MapNotInvertible is thrown if the bridge does not support inverting
+        # the function. The user doesn't need to know this, only that they
+        # cannot get the attribute.
         if err isa MOI.Bridges.MapNotInvertible
             throw(MOI.GetAttributeNotAllowed(attr))
-        else
-            rethrow(err)
         end
+        rethrow(err)
     end
     return MOI.Utilities.convert_approx(G, func)
 end
@@ -154,14 +156,16 @@ function MOI.get(
     if value === nothing
         return nothing
     end
-    return try
-        MOI.Bridges.inverse_map_function(bridge, value)
+    try
+        return MOI.Bridges.inverse_map_function(bridge, value)
     catch err
+        # MapNotInvertible is thrown if the bridge does not support inverting
+        # the function. The user doesn't need to know this, only that they
+        # cannot get the attribute.
         if err isa MOI.Bridges.MapNotInvertible
             throw(MOI.GetAttributeNotAllowed(attr))
-        else
-            rethrow(err)
         end
+        rethrow(err)
     end
 end
 
diff --git a/src/Bridges/set_map.jl b/src/Bridges/set_map.jl
index 094ef03d4f..03583ee8e3 100644
--- a/src/Bridges/set_map.jl
+++ b/src/Bridges/set_map.jl
@@ -34,16 +34,25 @@ used for getting the [`MOI.ConstraintSet`](@ref).
 function inverse_map_set end
 
 """
+    map_function(bridge::MOI.Bridges.AbstractBridge, func)
     map_function(::Type{BT}, func) where {BT}
 
 Return the image of `func` through the linear map `A` defined in
-[`Variable.SetMapBridge`](@ref) and [`Constraint.SetMapBridge`](@ref). This is
-used for getting the [`MOI.ConstraintPrimal`](@ref) of variable
+[`Variable.SetMapBridge`](@ref) and [`Constraint.SetMapBridge`](@ref).
+
+This function is used for getting the [`MOI.ConstraintPrimal`](@ref) of variable
 bridges. For constraint bridges, this is used for bridging the constraint,
-setting the [`MOI.ConstraintFunction`](@ref) and
-[`MOI.ConstraintPrimalStart`](@ref) and
-modifying the function with [`MOI.modify`](@ref).
+setting the [`MOI.ConstraintFunction`](@ref) and [`MOI.ConstraintPrimalStart`](@ref)
+and modifying the function with [`MOI.modify`](@ref).
+
+The method can alternatively be defined on the bridge type. This legacy
+interface is kept for backward compatibility.
+"""
+function map_function(bridge::AbstractBridge, func)
+    return map_function(typeof(bridge), func)
+end
 
+"""
     map_function(::Type{BT}, func, i::IndexInVector) where {BT}
 
 Return the scalar function at the `i`th index of the vector function that
@@ -52,77 +61,65 @@ would be returned by `map_function(BT, func)` except that it may compute the
 the [`MOI.VariablePrimal`](@ref) and
 [`MOI.VariablePrimalStart`](@ref) of variable bridges.
 """
-function map_function end
-
-function map_function(bridge::AbstractBridge, func)
-    return map_function(typeof(bridge), func)
-end
-
 function map_function(::Type{BT}, func, i::IndexInVector) where {BT}
     return MOI.Utilities.eachscalar(map_function(BT, func))[i.value]
 end
 
 """
     inverse_map_function(bridge::MOI.Bridges.AbstractBridge, func)
+    inverse_map_function(::Type{BT}, func) where {BT}
 
 Return the image of `func` through the inverse of the linear map `A` defined in
-[`Variable.SetMapBridge`](@ref) and [`Constraint.SetMapBridge`](@ref). This is
-used by [`Variable.unbridged_map`](@ref) and for setting the
-[`MOI.VariablePrimalStart`](@ref) of variable bridges
-and for getting the [`MOI.ConstraintFunction`](@ref),
-the [`MOI.ConstraintPrimal`](@ref) and the
+[`Variable.SetMapBridge`](@ref) and [`Constraint.SetMapBridge`](@ref).
+
+This function is used by [`Variable.unbridged_map`](@ref) and for setting the
+[`MOI.VariablePrimalStart`](@ref) of variable bridges and for getting the
+[`MOI.ConstraintFunction`](@ref), the [`MOI.ConstraintPrimal`](@ref) and the
 [`MOI.ConstraintPrimalStart`](@ref) of constraint bridges.
+
 If the linear map `A` is not invertible, the error [`MapNotInvertible`](@ref) is
 thrown.
 
-    inverse_map_function(::Type{BT}, func) where {BT}
-
 The method can alternatively be defined on the bridge type. This legacy
 interface is kept for backward compatibility.
 """
-function inverse_map_function end
-
 function inverse_map_function(bridge::AbstractBridge, func)
     return inverse_map_function(typeof(bridge), func)
 end
 
 """
     adjoint_map_function(bridge::MOI.Bridges.AbstractBridge, func)
+    adjoint_map_function(::Type{BT}, func) where {BT}
 
 Return the image of `func` through the adjoint of the linear map `A` defined in
-[`Variable.SetMapBridge`](@ref) and [`Constraint.SetMapBridge`](@ref). This is
-used for getting the [`MOI.ConstraintDual`](@ref) and
-[`MOI.ConstraintDualStart`](@ref) of constraint bridges.
+[`Variable.SetMapBridge`](@ref) and [`Constraint.SetMapBridge`](@ref).
 
-    adjoint_map_function(::Type{BT}, func) where {BT}
+This function is used for getting the [`MOI.ConstraintDual`](@ref) and
+[`MOI.ConstraintDualStart`](@ref) of constraint bridges.
 
 The method can alternatively be defined on the bridge type. This legacy
 interface is kept for backward compatibility.
 """
-function adjoint_map_function end
-
 function adjoint_map_function(bridge::AbstractBridge, func)
     return adjoint_map_function(typeof(bridge), func)
 end
 
 """
     inverse_adjoint_map_function(bridge::MOI.Bridges.AbstractBridge, func)
+    inverse_adjoint_map_function(::Type{BT}, func) where {BT}
 
 Return the image of `func` through the inverse of the adjoint of the linear map
-`A` defined in [`Variable.SetMapBridge`](@ref) and
-[`Constraint.SetMapBridge`](@ref). This is used for getting the
-[`MOI.ConstraintDual`](@ref) of variable bridges and setting the
-[`MOI.ConstraintDualStart`](@ref) of constraint bridges.
+`A` defined in [`Variable.SetMapBridge`](@ref) and [`Constraint.SetMapBridge`](@ref).
+
+This function is used for getting the [`MOI.ConstraintDual`](@ref) of variable
+bridges and setting the [`MOI.ConstraintDualStart`](@ref) of constraint bridges.
+
 If the linear map `A` is not invertible, the error [`MapNotInvertible`](@ref) is
 thrown.
 
-    inverse_adjoint_map_function(::Type{BT}, func) where {BT}
-
 The method can alternatively be defined on the bridge type. This legacy
 interface is kept for backward compatibility.
 """
-function inverse_adjoint_map_function end
-
 function inverse_adjoint_map_function(bridge::AbstractBridge, func)
     return inverse_adjoint_map_function(typeof(bridge), func)
 end