diff --git a/src/ReachSets/AbstractReachSet.jl b/src/ReachSets/AbstractReachSet.jl
index 6793c5f7c..1006a0d8e 100644
--- a/src/ReachSets/AbstractReachSet.jl
+++ b/src/ReachSets/AbstractReachSet.jl
@@ -258,16 +258,22 @@ end
 # Concrete intersection methods
 # ------------------------------
 
-function intersection(R::AbstractReachSet, S::AbstractReachSet)
-    return _intersection(set(R), set(S), FallbackIntersection())
-end
-function _intersection(R::AbstractReachSet, S::AbstractReachSet, method::AbstractIntersectionMethod)
-    return _intersection(set(R), set(S), method)
+function intersection(R::AbstractReachSet, S::AbstractReachSet,
+                      method::AbstractIntersectionMethod=FallbackIntersection())
+    T1 = tspan(R)
+    T2 = tspan(S)
+    T = T1 ∩ T2
+    if isempty(T)
+        throw(ArgumentError("cannot intersect reach sets with disjoint time intervals"))
+    end
+
+    cap = _intersection(set(R), set(S), method)
+    return ReachSet(cap, T)
 end
 
 # fallback methods for reach-sets
 @commutative function _intersection(R::AbstractReachSet, X::LazySet,
-                                    method::AbstractIntersectionMethod)
+                                    method::AbstractIntersectionMethod=FallbackIntersection())
     return _intersection(set(R), X, method)
 end
 
diff --git a/src/ReachSets/TaylorModelReachSet.jl b/src/ReachSets/TaylorModelReachSet.jl
index 06030a2ba..9f28ed2df 100644
--- a/src/ReachSets/TaylorModelReachSet.jl
+++ b/src/ReachSets/TaylorModelReachSet.jl
@@ -69,10 +69,6 @@ end
 # ======================
 
 # for TMs, we overapproximate with a zonotope
-function _intersection(R::TaylorModelReachSet, Y::LazySet)
-    return _intersection(R, Y, FallbackIntersection())
-end
-
 function _intersection(R::TaylorModelReachSet, Y::LazySet, ::FallbackIntersection)
     X = set(overapproximate(R, Zonotope))
     return intersection(X, Y)