diff --git a/include/iris/interval_set.hpp b/include/iris/interval_set.hpp
index d7797e6..fe798ed 100644
--- a/include/iris/interval_set.hpp
+++ b/include/iris/interval_set.hpp
@@ -88,7 +88,16 @@ class interval_set
 
     constexpr interval_set() = default;
 
-    constexpr explicit interval_set(std::initializer_list<IntervalT> il)
+    // Unlike `std::vector` etc., we allow construction from a single `IntervalT`:
+    // an interval is not an element but a convex set of offsets.
+    constexpr explicit interval_set(IntervalT const& iv)
+    {
+        if (!iv.empty()) {
+            map_.emplace(iv.lower, iv.upper);
+        }
+    }
+
+    constexpr interval_set(std::initializer_list<IntervalT> il)
     {
         auto it = il.begin();
         if (it == il.end()) return;
diff --git a/test/interval_set.cpp b/test/interval_set.cpp
index ff8c1e4..8950834 100644
--- a/test/interval_set.cpp
+++ b/test/interval_set.cpp
@@ -35,8 +35,10 @@ TEST_CASE("interval_set: type_traits")
     STATIC_CHECK(std::is_copy_assignable_v<IVS>);
     STATIC_CHECK(std::is_nothrow_swappable_v<IVS>);
 
-    STATIC_CHECK(!std::is_constructible_v<IVS, interval<int>>);
+    STATIC_CHECK(std::is_constructible_v<IVS, interval<int>>);
+    STATIC_CHECK(!std::is_convertible_v<interval<int>, IVS>);
     STATIC_CHECK(std::is_constructible_v<IVS, std::initializer_list<interval<int>>>);
+    STATIC_CHECK(std::is_convertible_v<std::initializer_list<interval<int>>, IVS>);
 }
 
 TEST_CASE("interval_set: construction")