diff --git a/src/Approximations/overapproximate.jl b/src/Approximations/overapproximate.jl
index e1a6e19477..fe998fc2f9 100644
--- a/src/Approximations/overapproximate.jl
+++ b/src/Approximations/overapproximate.jl
@@ -23,6 +23,26 @@ function overapproximate(X::S, ::Type{S}, args...; kwargs...) where {S<:LazySet}
     return X
 end
 
+"""
+    overapproximate(S::LazySet, T::Type{<:LazySet}, [args]...; [kwargs]...)
+
+Default overapproximation method that falls back to `convert`.
+
+### Input
+
+- `X`       -- set
+- `Type{S}` -- target set type
+- `args`    -- further arguments
+- `kwargs`  -- further keyword arguments
+
+### Output
+
+The result of `convert`, or a `MethodError` if no such method exists.
+"""
+function overapproximate(X::T1, T2::Type{<:LazySet}, args...; kwargs...) where {T1<:LazySet}
+    return convert(T2, X, args...; kwargs...)
+end
+
 """
     overapproximate(S::LazySet)
 
@@ -130,9 +150,9 @@ for ST in LazySets.subtypes(LazySet, true)
     end
     @eval overapproximate(∅::EmptySet, ::Type{<:$ST}) = ∅
 end
+overapproximate(∅::EmptySet, ::Type{<:LazySet}, args...; kwargs...) = ∅
 overapproximate(∅::EmptySet, ::Real) = ∅
 overapproximate(∅::EmptySet, ::Type{<:HPolygon}, ::Real=Inf; kwargs...) = ∅
-overapproximate(∅::EmptySet, ::Type{<:EmptySet}, args...; kwargs...) = ∅
 function overapproximate(∅::EmptySet, ::Type{<:Zonotope},
                          ::Union{AbstractDirections,Type{<:AbstractDirections}};
                          kwargs...)
diff --git a/src/Approximations/overapproximate_zonotope.jl b/src/Approximations/overapproximate_zonotope.jl
index 49a8a8ba09..c226bb35c6 100644
--- a/src/Approximations/overapproximate_zonotope.jl
+++ b/src/Approximations/overapproximate_zonotope.jl
@@ -209,26 +209,6 @@ function _overapproximate_convex_hull_zonotope_GGP09(X::ConvexHull{N}) where {N}
     return Zonotope(c, G)
 end
 
-"""
-    overapproximate(lm::LinearMap{N, <:AbstractZonotope},
-                    ::Type{<:Zonotope}) where {N}
-
-Overapproximate a lazy linear map of a zonotopic set with a zonotope.
-
-### Input
-
-- `lm`       -- lazy linear map of a zonotopic set
-- `Zonotope` -- target set type
-
-### Output
-
-The tight zonotope corresponding to `lm`.
-"""
-function overapproximate(lm::LinearMap{N,<:AbstractZonotope},
-                         ::Type{<:Zonotope}) where {N}
-    return convert(Zonotope, lm)
-end
-
 # Given center, (dependent) generator matrix and exponent matrix of a (simple)
 # sparse polynomial zonotope, compute thew new center and generator matrix of
 # its zonotope overapproximation.
diff --git a/test/Approximations/overapproximate.jl b/test/Approximations/overapproximate.jl
index eef1b8648d..7208cb3e32 100644
--- a/test/Approximations/overapproximate.jl
+++ b/test/Approximations/overapproximate.jl
@@ -16,6 +16,10 @@ for N in [Float64, Rational{Int}, Float32]
     oa = overapproximate(b, Ball1, Hyperrectangle)
     @test oa isa Ball1
 
+    # default fallback to `convert`
+    B = BallInf(c, N(1))
+    overapproximate(B, Zonotope) == Zonotope(c, N[1 0; 0 1])
+
     # HPolygon approximation with box directions
     p = overapproximate(b, HPolygon)
     for d in [N[1, 0], N[-1, 0]]