diff --git a/gsl/gsl_util b/gsl/gsl_util
index f0ac964..a8a41ae 100644
--- a/gsl/gsl_util
+++ b/gsl/gsl_util
@@ -48,6 +48,18 @@
 
 #endif // _MSC_VER
 
+// AFAIK there's no way to detect in GCC or MSVC. GCC has an __EXCEPTIONS macro,
+// but that is only defined if `-fexceptions` is *explicitly* passed on the
+// command line; defaulting to exceptions enabled will not set this macro.
+//
+// Non-Clang users will need to defined GSL_NO_EXCEPTIONS explicitly from the
+// command line if they are building with exceptions disabled.
+#if defined(__clang__) && !__has_feature(cxx_exceptions)
+// If building with -fno-exceptions, we'll fall back to gsl::Ensures in places
+// where we would have normally thrown an exception.
+#define GSL_NO_EXCEPTIONS
+#endif // defined(__has_feature) && !__has_feature(cxx_exceptions)
+
 namespace gsl
 {
 //
@@ -125,9 +137,14 @@
 inline T narrow(U u)
 {
     T t = narrow_cast<T>(u);
+#ifndef GSL_NO_EXCEPTIONS
     if (static_cast<U>(t) != u) throw narrowing_error();
     if (!details::is_same_signedness<T, U>::value && ((t < T{}) != (u < U{})))
         throw narrowing_error();
+#else
+    Ensures(static_cast<U>(t) == u);
+    Ensures(!(!details::is_same_signedness<T, U>::value && ((t < T{}) != (u < U{}))));
+#endif
     return t;
 }
 
@@ -135,30 +152,30 @@
 // at() - Bounds-checked way of accessing static arrays, std::array, std::vector
 //
 template <class T, size_t N>
-constexpr T& at(T (&arr)[N], size_t index)
+constexpr T& at(T (&arr)[N], std::ptrdiff_t index)
 {
-    Expects(index < N);
-    return arr[index];
+    Expects(index >= 0 && index < narrow_cast<std::ptrdiff_t>(N));
+    return arr[static_cast<size_t>(index)];
 }
 
 template <class T, size_t N>
-constexpr T& at(std::array<T, N>& arr, size_t index)
+constexpr T& at(std::array<T, N>& arr, std::ptrdiff_t index)
 {
-    Expects(index < N);
-    return arr[index];
+    Expects(index >= 0 && index < narrow_cast<std::ptrdiff_t>(N));
+    return arr[static_cast<size_t>(index)];
 }
 
 template <class Cont>
-constexpr typename Cont::value_type& at(Cont& cont, size_t index)
+constexpr typename Cont::value_type& at(Cont& cont, std::ptrdiff_t index)
 {
-    Expects(index < cont.size());
-    return cont[index];
+    Expects(index >= 0 && index < narrow_cast<std::ptrdiff_t>(cont.size()));
+    return cont[static_cast<typename Cont::size_type>(index)];
 }
 
 template <class T>
-constexpr const T& at(std::initializer_list<T> cont, size_t index)
+constexpr const T& at(std::initializer_list<T> cont, std::ptrdiff_t index)
 {
-    Expects(index < cont.size());
+    Expects(index >= 0 && index < narrow_cast<std::ptrdiff_t>(cont.size()));
     return *(cont.begin() + index);
 }