diff --git a/src/libexpr/eval.cc b/src/libexpr/eval.cc
index b4b4f7b5c..641687f2a 100644
--- a/src/libexpr/eval.cc
+++ b/src/libexpr/eval.cc
@@ -787,7 +787,7 @@ void mkPath(Value & v, const char * s)
 
 inline Value * EvalState::lookupVar(Env * env, const ExprVar & var, bool noEval)
 {
-    for (size_t l = var.level; l; --l, env = env->up) ;
+    for (auto l = var.level; l; --l, env = env->up) ;
 
     if (!var.fromWith) return env->values[var.displ];
 
@@ -1060,7 +1060,7 @@ void ExprAttrs::eval(EvalState & state, Env & env, Value & v)
         /* The recursive attributes are evaluated in the new
            environment, while the inherited attributes are evaluated
            in the original environment. */
-        size_t displ = 0;
+        Displacement displ = 0;
         for (auto & i : attrs) {
             Value * vAttr;
             if (hasOverrides && !i.second.inherited) {
@@ -1136,7 +1136,7 @@ void ExprLet::eval(EvalState & state, Env & env, Value & v)
     /* The recursive attributes are evaluated in the new environment,
        while the inherited attributes are evaluated in the original
        environment. */
-    size_t displ = 0;
+    Displacement displ = 0;
     for (auto & i : attrs->attrs)
         env2.values[displ++] = i.second.e->maybeThunk(state, i.second.inherited ? env : env2);
 
@@ -1283,7 +1283,7 @@ void EvalState::callFunction(Value & fun, size_t nrArgs, Value * * args, Value &
             Env & env2(allocEnv(size));
             env2.up = vCur.lambda.env;
 
-            size_t displ = 0;
+            Displacement displ = 0;
 
             if (!lambda.hasFormals())
                 env2.values[displ++] = args[0];
diff --git a/src/libexpr/nixexpr.cc b/src/libexpr/nixexpr.cc
index 372e323bc..57c2f6e44 100644
--- a/src/libexpr/nixexpr.cc
+++ b/src/libexpr/nixexpr.cc
@@ -273,7 +273,7 @@ void ExprVar::bindVars(const StaticEnv & env)
     /* Check whether the variable appears in the environment.  If so,
        set its level and displacement. */
     const StaticEnv * curEnv;
-    unsigned int level;
+    Level level;
     int withLevel = -1;
     for (curEnv = &env, level = 0; curEnv; curEnv = curEnv->up, level++) {
         if (curEnv->isWith) {
@@ -326,7 +326,7 @@ void ExprAttrs::bindVars(const StaticEnv & env)
     if (recursive) {
         dynamicEnv = &newEnv;
 
-        unsigned int displ = 0;
+        Displacement displ = 0;
         for (auto & i : attrs)
             newEnv.vars.emplace_back(i.first, i.second.displ = displ++);
 
@@ -359,7 +359,7 @@ void ExprLambda::bindVars(const StaticEnv & env)
         (hasFormals() ? formals->formals.size() : 0) +
         (arg.empty() ? 0 : 1));
 
-    unsigned int displ = 0;
+    Displacement displ = 0;
 
     if (!arg.empty()) newEnv.vars.emplace_back(arg, displ++);
 
@@ -387,7 +387,7 @@ void ExprLet::bindVars(const StaticEnv & env)
 {
     StaticEnv newEnv(false, &env, attrs->attrs.size());
 
-    unsigned int displ = 0;
+    Displacement displ = 0;
     for (auto & i : attrs->attrs)
         newEnv.vars.emplace_back(i.first, i.second.displ = displ++);
 
@@ -405,7 +405,7 @@ void ExprWith::bindVars(const StaticEnv & env)
        level so that `lookupVar' can look up variables in the previous
        `with' if this one doesn't contain the desired attribute. */
     const StaticEnv * curEnv;
-    unsigned int level;
+    Level level;
     prevWith = 0;
     for (curEnv = &env, level = 1; curEnv; curEnv = curEnv->up, level++)
         if (curEnv->isWith) {
diff --git a/src/libexpr/nixexpr.hh b/src/libexpr/nixexpr.hh
index fe12890e9..13256272c 100644
--- a/src/libexpr/nixexpr.hh
+++ b/src/libexpr/nixexpr.hh
@@ -133,6 +133,9 @@ struct ExprPath : Expr
     Value * maybeThunk(EvalState & state, Env & env);
 };
 
+typedef uint32_t Level;
+typedef uint32_t Displacement;
+
 struct ExprVar : Expr
 {
     Pos pos;
@@ -148,8 +151,8 @@ struct ExprVar : Expr
        value is obtained by getting the attribute named `name' from
        the set stored in the environment that is `level' levels up
        from the current one.*/
-    unsigned int level;
-    unsigned int displ;
+    Level level;
+    Displacement displ;
 
     ExprVar(const Symbol & name) : name(name) { };
     ExprVar(const Pos & pos, const Symbol & name) : pos(pos), name(name) { };
@@ -183,7 +186,7 @@ struct ExprAttrs : Expr
         bool inherited;
         Expr * e;
         Pos pos;
-        unsigned int displ; // displacement
+        Displacement displ; // displacement
         AttrDef(Expr * e, const Pos & pos, bool inherited=false)
             : inherited(inherited), e(e), pos(pos) { };
         AttrDef() { };
@@ -352,7 +355,7 @@ struct StaticEnv
     const StaticEnv * up;
 
     // Note: these must be in sorted order.
-    typedef std::vector<std::pair<Symbol, unsigned int>> Vars;
+    typedef std::vector<std::pair<Symbol, Displacement>> Vars;
     Vars vars;
 
     StaticEnv(bool isWith, const StaticEnv * up, size_t expectedSize = 0) : isWith(isWith), up(up) {