diff --git a/src/librustc/infer/higher_ranked/mod.rs b/src/librustc/infer/higher_ranked/mod.rs
index d44f2ec95492f..c6e7147c58abe 100644
--- a/src/librustc/infer/higher_ranked/mod.rs
+++ b/src/librustc/infer/higher_ranked/mod.rs
@@ -417,7 +417,7 @@ impl<'a, 'gcx, 'tcx> CombineFields<'a, 'gcx, 'tcx> {
         {
             for (a_br, a_r) in a_map {
                 if *a_r == r {
-                    return infcx.tcx.mk_region(ty::ReLateBound(ty::DebruijnIndex::new(1), *a_br));
+                    return infcx.tcx.mk_region(ty::ReLateBound(ty::DebruijnIndex::new(0), *a_br));
                 }
             }
             span_bug!(
diff --git a/src/librustc/middle/resolve_lifetime.rs b/src/librustc/middle/resolve_lifetime.rs
index ceda72dcd7ae0..e5bb63f5d1f85 100644
--- a/src/librustc/middle/resolve_lifetime.rs
+++ b/src/librustc/middle/resolve_lifetime.rs
@@ -98,7 +98,7 @@ impl Region {
     }
 
     fn late(hir_map: &Map, def: &hir::LifetimeDef) -> (hir::LifetimeName, Region) {
-        let depth = ty::DebruijnIndex::new(1);
+        let depth = ty::DebruijnIndex::new(0);
         let def_id = hir_map.local_def_id(def.lifetime.id);
         let origin = LifetimeDefOrigin::from_is_in_band(def.in_band);
         (def.lifetime.name, Region::LateBound(depth, def_id, origin))
@@ -107,7 +107,7 @@ impl Region {
     fn late_anon(index: &Cell<u32>) -> Region {
         let i = index.get();
         index.set(i + 1);
-        let depth = ty::DebruijnIndex::new(1);
+        let depth = ty::DebruijnIndex::new(0);
         Region::LateBoundAnon(depth, i)
     }
 
@@ -137,14 +137,14 @@ impl Region {
         match self {
             Region::LateBound(debruijn, id, origin) => Region::LateBound(
                 ty::DebruijnIndex {
-                    depth: debruijn.depth - (depth - 1),
+                    depth: debruijn.depth - depth,
                 },
                 id,
                 origin,
             ),
             Region::LateBoundAnon(debruijn, index) => Region::LateBoundAnon(
                 ty::DebruijnIndex {
-                    depth: debruijn.depth - (depth - 1),
+                    depth: debruijn.depth - depth,
                 },
                 index,
             ),
@@ -1781,7 +1781,7 @@ impl<'a, 'tcx> LifetimeContext<'a, 'tcx> {
             .map(|(i, input)| {
                 let mut gather = GatherLifetimes {
                     map: self.map,
-                    binder_depth: 1,
+                    binder_depth: 0,
                     have_bound_regions: false,
                     lifetimes: FxHashSet(),
                 };
diff --git a/src/librustc/ty/fold.rs b/src/librustc/ty/fold.rs
index 8071cd0c639da..d98b5fa35fdab 100644
--- a/src/librustc/ty/fold.rs
+++ b/src/librustc/ty/fold.rs
@@ -292,7 +292,7 @@ impl<'a, 'gcx, 'tcx> RegionFolder<'a, 'gcx, 'tcx> {
         RegionFolder {
             tcx,
             skipped_regions,
-            current_depth: 1,
+            current_depth: 0,
             fld_r,
         }
     }
@@ -448,7 +448,7 @@ impl<'a, 'gcx, 'tcx> TyCtxt<'a, 'gcx, 'tcx> {
         let mut counter = 0;
         Binder(self.replace_late_bound_regions(sig, |_| {
             counter += 1;
-            self.mk_region(ty::ReLateBound(ty::DebruijnIndex::new(1), ty::BrAnon(counter)))
+            self.mk_region(ty::ReLateBound(ty::DebruijnIndex::new(0), ty::BrAnon(counter)))
         }).0)
     }
 }
@@ -460,7 +460,7 @@ impl<'a, 'gcx, 'tcx> RegionReplacer<'a, 'gcx, 'tcx> {
     {
         RegionReplacer {
             tcx,
-            current_depth: 1,
+            current_depth: 0,
             fld_r,
             map: BTreeMap::default()
         }
@@ -478,7 +478,7 @@ impl<'a, 'gcx, 'tcx> TypeFolder<'gcx, 'tcx> for RegionReplacer<'a, 'gcx, 'tcx> {
     }
 
     fn fold_ty(&mut self, t: Ty<'tcx>) -> Ty<'tcx> {
-        if !t.has_regions_escaping_depth(self.current_depth-1) {
+        if !t.has_regions_escaping_depth(self.current_depth) {
             return t;
         }
 
@@ -635,7 +635,7 @@ struct LateBoundRegionsCollector {
 impl LateBoundRegionsCollector {
     fn new(just_constrained: bool) -> Self {
         LateBoundRegionsCollector {
-            current_depth: 1,
+            current_depth: 0,
             regions: FxHashSet(),
             just_constrained,
         }
diff --git a/src/librustc/ty/sty.rs b/src/librustc/ty/sty.rs
index ed04d41ba1457..12e15129cbaeb 100644
--- a/src/librustc/ty/sty.rs
+++ b/src/librustc/ty/sty.rs
@@ -1156,7 +1156,6 @@ impl<'a, 'tcx, 'gcx> PolyExistentialProjection<'tcx> {
 
 impl DebruijnIndex {
     pub fn new(depth: u32) -> DebruijnIndex {
-        assert!(depth > 0);
         DebruijnIndex { depth: depth }
     }
 
@@ -1188,11 +1187,11 @@ impl RegionKind {
         }
     }
 
-    /// Returns the depth of `self` from the (1-based) binding level `depth`
+    /// Returns the depth of `self` from the (0-based) binding level `depth`
     pub fn from_depth(&self, depth: u32) -> RegionKind {
         match *self {
             ty::ReLateBound(debruijn, r) => ty::ReLateBound(DebruijnIndex {
-                depth: debruijn.depth - (depth - 1)
+                depth: debruijn.depth - depth
             }, r),
             r => r
         }
diff --git a/src/librustc/ty/util.rs b/src/librustc/ty/util.rs
index 22f851a908b25..17b1e4be2082c 100644
--- a/src/librustc/ty/util.rs
+++ b/src/librustc/ty/util.rs
@@ -589,7 +589,7 @@ impl<'a, 'gcx, 'tcx> TyCtxt<'a, 'gcx, 'tcx> {
                           -> Option<ty::Binder<Ty<'tcx>>>
     {
         let closure_ty = self.mk_closure(closure_def_id, closure_substs);
-        let env_region = ty::ReLateBound(ty::DebruijnIndex::new(1), ty::BrEnv);
+        let env_region = ty::ReLateBound(ty::DebruijnIndex::new(0), ty::BrEnv);
         let closure_kind_ty = closure_substs.closure_kind_ty(closure_def_id, self);
         let closure_kind = closure_kind_ty.to_opt_closure_kind()?;
         let env_ty = match closure_kind {
diff --git a/src/librustc/util/ppaux.rs b/src/librustc/util/ppaux.rs
index d27cda4040e56..6f99b6ecf5ebf 100644
--- a/src/librustc/util/ppaux.rs
+++ b/src/librustc/util/ppaux.rs
@@ -497,7 +497,7 @@ impl PrintContext {
                                 name)
                 }
             };
-            tcx.mk_region(ty::ReLateBound(ty::DebruijnIndex::new(1), br))
+            tcx.mk_region(ty::ReLateBound(ty::DebruijnIndex::new(0), br))
         }).0;
         start_or_continue(f, "", "> ")?;
 
diff --git a/src/librustc_driver/test.rs b/src/librustc_driver/test.rs
index 9efd8844977f9..729960a7655d4 100644
--- a/src/librustc_driver/test.rs
+++ b/src/librustc_driver/test.rs
@@ -327,7 +327,7 @@ impl<'a, 'gcx, 'tcx> Env<'a, 'gcx, 'tcx> {
     }
 
     pub fn t_rptr_late_bound(&self, id: u32) -> Ty<'tcx> {
-        let r = self.re_late_bound_with_debruijn(id, ty::DebruijnIndex::new(1));
+        let r = self.re_late_bound_with_debruijn(id, ty::DebruijnIndex::new(0));
         self.infcx.tcx.mk_imm_ref(r, self.tcx().types.isize)
     }
 
@@ -484,7 +484,7 @@ fn subst_ty_renumber_bound() {
 
         // t_expected = fn(&'a isize)
         let t_expected = {
-            let t_ptr_bound2 = env.t_rptr_late_bound_with_debruijn(1, ty::DebruijnIndex::new(2));
+            let t_ptr_bound2 = env.t_rptr_late_bound_with_debruijn(1, ty::DebruijnIndex::new(1));
             env.t_fn(&[t_ptr_bound2], env.t_nil())
         };
 
@@ -521,7 +521,7 @@ fn subst_ty_renumber_some_bounds() {
         //
         // but not that the Debruijn index is different in the different cases.
         let t_expected = {
-            let t_rptr_bound2 = env.t_rptr_late_bound_with_debruijn(1, ty::DebruijnIndex::new(2));
+            let t_rptr_bound2 = env.t_rptr_late_bound_with_debruijn(1, ty::DebruijnIndex::new(1));
             env.t_pair(t_rptr_bound1, env.t_fn(&[t_rptr_bound2], env.t_nil()))
         };
 
@@ -549,10 +549,10 @@ fn escaping() {
         let t_rptr_free1 = env.t_rptr_free(1);
         assert!(!t_rptr_free1.has_escaping_regions());
 
-        let t_rptr_bound1 = env.t_rptr_late_bound_with_debruijn(1, ty::DebruijnIndex::new(1));
+        let t_rptr_bound1 = env.t_rptr_late_bound_with_debruijn(1, ty::DebruijnIndex::new(0));
         assert!(t_rptr_bound1.has_escaping_regions());
 
-        let t_rptr_bound2 = env.t_rptr_late_bound_with_debruijn(1, ty::DebruijnIndex::new(2));
+        let t_rptr_bound2 = env.t_rptr_late_bound_with_debruijn(1, ty::DebruijnIndex::new(1));
         assert!(t_rptr_bound2.has_escaping_regions());
 
         // t_fn = fn(A)
@@ -568,7 +568,7 @@ fn escaping() {
 #[test]
 fn subst_region_renumber_region() {
     test_env(EMPTY_SOURCE_STR, errors(&[]), |env| {
-        let re_bound1 = env.re_late_bound_with_debruijn(1, ty::DebruijnIndex::new(1));
+        let re_bound1 = env.re_late_bound_with_debruijn(1, ty::DebruijnIndex::new(0));
 
         // type t_source<'a> = fn(&'a isize)
         let t_source = {
@@ -583,7 +583,7 @@ fn subst_region_renumber_region() {
         //
         // but not that the Debruijn index is different in the different cases.
         let t_expected = {
-            let t_rptr_bound2 = env.t_rptr_late_bound_with_debruijn(1, ty::DebruijnIndex::new(2));
+            let t_rptr_bound2 = env.t_rptr_late_bound_with_debruijn(1, ty::DebruijnIndex::new(1));
             env.t_fn(&[t_rptr_bound2], env.t_nil())
         };
 
diff --git a/src/librustc_trans/common.rs b/src/librustc_trans/common.rs
index e83e73c8ae757..8f1102c1e4791 100644
--- a/src/librustc_trans/common.rs
+++ b/src/librustc_trans/common.rs
@@ -425,7 +425,7 @@ pub fn ty_fn_sig<'a, 'tcx>(cx: &CodegenCx<'a, 'tcx>,
             let tcx = cx.tcx;
             let sig = substs.generator_poly_sig(def_id, cx.tcx);
 
-            let env_region = ty::ReLateBound(ty::DebruijnIndex::new(1), ty::BrEnv);
+            let env_region = ty::ReLateBound(ty::DebruijnIndex::new(0), ty::BrEnv);
             let env_ty = tcx.mk_mut_ref(tcx.mk_region(env_region), ty);
 
             sig.map_bound(|sig| {
diff --git a/src/librustc_typeck/check/intrinsic.rs b/src/librustc_typeck/check/intrinsic.rs
index 377e3a891840f..006ccc3c6d1d9 100644
--- a/src/librustc_typeck/check/intrinsic.rs
+++ b/src/librustc_typeck/check/intrinsic.rs
@@ -119,7 +119,7 @@ pub fn check_intrinsic_type<'a, 'tcx>(tcx: TyCtxt<'a, 'tcx, 'tcx>,
             "pref_align_of" | "min_align_of" => (1, Vec::new(), tcx.types.usize),
             "size_of_val" |  "min_align_of_val" => {
                 (1, vec![
-                    tcx.mk_imm_ref(tcx.mk_region(ty::ReLateBound(ty::DebruijnIndex::new(1),
+                    tcx.mk_imm_ref(tcx.mk_region(ty::ReLateBound(ty::DebruijnIndex::new(0),
                                                                   ty::BrAnon(0))),
                                     param(0))
                  ], tcx.types.usize)
@@ -298,7 +298,7 @@ pub fn check_intrinsic_type<'a, 'tcx>(tcx: TyCtxt<'a, 'tcx, 'tcx>,
             "unlikely" => (0, vec![tcx.types.bool], tcx.types.bool),
 
             "discriminant_value" => (1, vec![
-                    tcx.mk_imm_ref(tcx.mk_region(ty::ReLateBound(ty::DebruijnIndex::new(1),
+                    tcx.mk_imm_ref(tcx.mk_region(ty::ReLateBound(ty::DebruijnIndex::new(0),
                                                                   ty::BrAnon(0))),
                                    param(0))], tcx.types.u64),