diff --git a/src/Approximations/overapproximate.jl b/src/Approximations/overapproximate.jl
index d771bcf83c..f2befa89dc 100644
--- a/src/Approximations/overapproximate.jl
+++ b/src/Approximations/overapproximate.jl
@@ -305,5 +305,5 @@ function overapproximate(cap::Intersection{N,
                          dir::AbstractDirections{N};
                          kwargs...
                         ) where {N<:Real}
-    return overapproximate(cap.Y ∩ cap.X, dir; kwargs...)
+    return overapproximate(swap(cap), dir; kwargs...)
 end
diff --git a/src/Intersection.jl b/src/Intersection.jl
index 4f98c6f1be..983f2eada2 100644
--- a/src/Intersection.jl
+++ b/src/Intersection.jl
@@ -379,7 +379,7 @@ function ρ(d::AbstractVector{N},
                              <:LazySet{N}};
            algorithm::String="line_search",
            kwargs...) where N<:Real
-    return ρ_helper(d, cap.Y ∩ cap.X, algorithm; kwargs...)
+    return ρ_helper(d, swap(cap), algorithm; kwargs...)
 end
 
 """
@@ -435,7 +435,7 @@ end
 function ρ(d::AbstractVector{N},
            cap::Intersection{N, <:AbstractPolytope{N}, <:LazySet{N}};
            kwargs...) where {N<:Real}
-    return ρ(d, cap.Y ∩ cap.X; kwargs...)
+    return ρ(d, swap(cap); kwargs...)
 end
 
 # disambiguation
@@ -464,7 +464,7 @@ function ρ(d::AbstractVector{N},
                              <:AbstractPolytope{N}};
            algorithm::String="line_search",
            kwargs...) where N<:Real
-    return ρ_helper(d, cap.Y ∩ cap.X, algorithm; kwargs...)
+    return ρ_helper(d, swap(cap), algorithm; kwargs...)
 end
 
 """