diff --git a/src/librustc/mir/interpret/mod.rs b/src/librustc/mir/interpret/mod.rs
index 6c31d54e081c4..d2c97221bf03e 100644
--- a/src/librustc/mir/interpret/mod.rs
+++ b/src/librustc/mir/interpret/mod.rs
@@ -123,7 +123,10 @@ use rustc_data_structures::tiny_list::TinyList;
 use rustc_macros::HashStable;
 use byteorder::{WriteBytesExt, ReadBytesExt, LittleEndian, BigEndian};
 
-/// Uniquely identifies a specific constant or static.
+/// Uniquely identifies one of the following:
+/// - A constant
+/// - A static
+/// - A const fn where all arguments (if any) are zero-sized types
 #[derive(Copy, Clone, Debug, Eq, PartialEq, Hash, RustcEncodable, RustcDecodable, HashStable)]
 pub struct GlobalId<'tcx> {
     /// For a constant or static, the `Instance` of the item itself.
diff --git a/src/librustc_mir/interpret/terminator.rs b/src/librustc_mir/interpret/terminator.rs
index e10bb85d52df8..e6ccfe885b5be 100644
--- a/src/librustc_mir/interpret/terminator.rs
+++ b/src/librustc_mir/interpret/terminator.rs
@@ -7,7 +7,7 @@ use syntax::source_map::Span;
 use rustc_target::spec::abi::Abi;
 
 use super::{
-    InterpResult, PointerArithmetic,
+    GlobalId, InterpResult, PointerArithmetic,
     InterpCx, Machine, OpTy, ImmTy, PlaceTy, MPlaceTy, StackPopCleanup, FnVal,
 };
 
@@ -293,6 +293,31 @@ impl<'mir, 'tcx, M: Machine<'mir, 'tcx>> InterpCx<'mir, 'tcx, M> {
                     }
                 }
 
+                // If this function is a const function then as an optimisation we can query this
+                // evaluation immediately.
+                //
+                // For the moment we only do this for functions which take no arguments
+                // (or all arguments are ZSTs) so that we don't memoize too much.
+                if self.tcx.is_const_fn_raw(instance.def.def_id()) &&
+                   args.iter().all(|a| a.layout.is_zst())
+                {
+                    let gid = GlobalId { instance, promoted: None };
+                    let place = self.const_eval_raw(gid)?;
+
+                    let dest = match dest {
+                        Some(dest) => dest,
+                        None => throw_ub!(Unreachable)
+                    };
+
+                    self.copy_op(place.into(), dest)?;
+
+                    // No stack frame gets pushed, the main loop will just act as if the
+                    // call completed.
+                    self.goto_block(ret)?;
+                    self.dump_place(*dest);
+                    return Ok(())
+                }
+
                 // We need MIR for this fn
                 let body = match M::find_fn(self, instance, args, dest, ret)? {
                     Some(body) => body,