diff --git a/src/constraint_solver/constraint_solver.h b/src/constraint_solver/constraint_solver.h
index aa761a6f1e..e334c400b6 100644
--- a/src/constraint_solver/constraint_solver.h
+++ b/src/constraint_solver/constraint_solver.h
@@ -2867,6 +2867,9 @@ class Solver {
 
   // Internal.
   IntExpr* CastExpression(IntVar* const var) const;
+  bool IsADifference(IntExpr* expr,
+                     IntExpr** const left,
+                     IntExpr** const right);
 
   const string name_;
   const SolverParameters parameters_;
diff --git a/src/constraint_solver/expr_cst.cc b/src/constraint_solver/expr_cst.cc
index 7b81e96951..87d7066b7d 100644
--- a/src/constraint_solver/expr_cst.cc
+++ b/src/constraint_solver/expr_cst.cc
@@ -81,12 +81,24 @@ string EqualityExprCst::DebugString() const {
 
 Constraint* Solver::MakeEquality(IntExpr* const e, int64 v) {
   CHECK_EQ(this, e->solver());
-  return RevAlloc(new EqualityExprCst(this, e, v));
+  IntExpr* left = NULL;
+  IntExpr* right = NULL;
+  if (v == 0 && IsADifference(e, &left, &right)) {
+    return MakeEquality(left->Var(), right->Var());
+  } else {
+    return RevAlloc(new EqualityExprCst(this, e, v));
+  }
 }
 
 Constraint* Solver::MakeEquality(IntExpr* const e, int v) {
   CHECK_EQ(this, e->solver());
-  return RevAlloc(new EqualityExprCst(this, e, v));
+  IntExpr* left = NULL;
+  IntExpr* right = NULL;
+  if (v == 0 && IsADifference(e, &left, &right)) {
+    return MakeEquality(left->Var(), right->Var());
+  } else {
+    return RevAlloc(new EqualityExprCst(this, e, v));
+  }
 }
 
 //-----------------------------------------------------------------------------
@@ -289,12 +301,24 @@ string DiffCst::DebugString() const {
 
 Constraint* Solver::MakeNonEquality(IntVar* const e, int64 v) {
   CHECK_EQ(this, e->solver());
-  return RevAlloc(new DiffCst(this, e, v));
+  IntExpr* left = NULL;
+  IntExpr* right = NULL;
+  if (v == 0 && IsADifference(e, &left, &right)) {
+    return MakeNonEquality(left->Var(), right->Var());
+  } else {
+    return RevAlloc(new DiffCst(this, e, v));
+  }
 }
 
 Constraint* Solver::MakeNonEquality(IntVar* const e, int v) {
   CHECK_EQ(this, e->solver());
-  return RevAlloc(new DiffCst(this, e, v));
+  IntExpr* left = NULL;
+  IntExpr* right = NULL;
+  if (v == 0 && IsADifference(e, &left, &right)) {
+    return MakeNonEquality(left->Var(), right->Var());
+  } else {
+    return RevAlloc(new DiffCst(this, e, v));
+  }
 }
 // ----- is_equal_cst Constraint -----
 
@@ -350,6 +374,11 @@ class IsEqualCstCt : public CastConstraint {
 }  // namespace
 
 IntVar* Solver::MakeIsEqualCstVar(IntVar* const var, int64 value) {
+  IntExpr* left = NULL;
+  IntExpr* right = NULL;
+  if (value == 0 && IsADifference(var, &left, &right)) {
+    return MakeIsEqualVar(left, right);
+  }
   return var->IsEqual(value);
 }
 
@@ -378,7 +407,13 @@ Constraint* Solver::MakeIsEqualCstCt(IntVar* const var,
       var,
       value,
       ModelCache::VAR_CONSTANT_IS_EQUAL);
-  return RevAlloc(new IsEqualCstCt(this, var, value, boolvar));
+  IntExpr* left = NULL;
+  IntExpr* right = NULL;
+  if (value == 0 && IsADifference(var, &left, &right)) {
+    return MakeIsEqualCt(left, right, boolvar);
+  } else {
+    return RevAlloc(new IsEqualCstCt(this, var, value, boolvar));
+  }
 }
 
 // ----- is_diff_cst Constraint -----
@@ -438,6 +473,11 @@ class IsDiffCstCt : public CastConstraint {
 }  // namespace
 
 IntVar* Solver::MakeIsDifferentCstVar(IntVar* const var, int64 value) {
+  IntExpr* left = NULL;
+  IntExpr* right = NULL;
+  if (value == 0 && IsADifference(var, &left, &right)) {
+    return MakeIsDifferentVar(left, right);
+  }
   return var->IsDifferent(value);
 }
 
@@ -470,7 +510,13 @@ Constraint* Solver::MakeIsDifferentCstCt(IntVar* const var,
       var,
       value,
       ModelCache::VAR_CONSTANT_IS_NOT_EQUAL);
-  return RevAlloc(new IsDiffCstCt(this, var, value, boolvar));
+  IntExpr* left = NULL;
+  IntExpr* right = NULL;
+  if (value == 0 && IsADifference(var, &left, &right)) {
+    return MakeIsDifferentCt(left, right, boolvar);
+  } else {
+    return RevAlloc(new IsDiffCstCt(this, var, value, boolvar));
+  }
 }
 
 // ----- is_greater_equal_cst Constraint -----
diff --git a/src/constraint_solver/expressions.cc b/src/constraint_solver/expressions.cc
index 46118a544d..7e73d49389 100644
--- a/src/constraint_solver/expressions.cc
+++ b/src/constraint_solver/expressions.cc
@@ -3084,6 +3084,8 @@ class SubIntExpr : public BaseIntExpr {
     visitor->EndVisitIntegerExpression(ModelVisitor::kDifference, this);
   }
 
+  IntExpr* left() const { return left_; }
+  IntExpr* right() const { return right_; }
  private:
   IntExpr* const left_;
   IntExpr* const right_;
@@ -6786,4 +6788,22 @@ IntVar* BaseIntExpr::CastToVar() {
   LinkVarExpr(solver(), this, var);
   return var;
 }
+
+// Discovery methods
+bool Solver::IsADifference(IntExpr* expr,
+                           IntExpr** const left,
+                           IntExpr** const right) {
+
+  if (expr->IsVar()) {
+    IntVar* const expr_var = expr->Var();
+    expr = CastExpression(expr_var);
+  }
+  SubIntExpr* const sub_expr = dynamic_cast<SubIntExpr*>(expr);
+  if (sub_expr != NULL) {
+    *left = sub_expr->left();
+    *right = sub_expr->right();
+    return true;
+  }
+  return false;
+}
 }   // namespace operations_research
diff --git a/src/constraint_solver/range_cst.cc b/src/constraint_solver/range_cst.cc
index 28bde3f82b..1a701f732c 100644
--- a/src/constraint_solver/range_cst.cc
+++ b/src/constraint_solver/range_cst.cc
@@ -395,6 +395,11 @@ Constraint* Solver::MakeNonEquality(IntVar* const l, IntVar* const r) {
   CHECK(r != NULL) << "left expression NULL, maybe a bad cast";
   CHECK_EQ(this, l->solver());
   CHECK_EQ(this, r->solver());
+  if (l->Bound()) {
+    return MakeNonEquality(r, l->Min());
+  } else if (r->Bound()) {
+    return MakeNonEquality(l, r->Min());
+  }
   return RevAlloc(new DiffVar(this, l, r));
 }
 
diff --git a/src/flatzinc/parser.cc b/src/flatzinc/parser.cc
index 79529c9edb..22a5a48720 100644
--- a/src/flatzinc/parser.cc
+++ b/src/flatzinc/parser.cc
@@ -809,6 +809,44 @@ bool ParserState::Presolve(CtSpec* const spec) {
     spec->ReplaceArg(2, new AST::IntLit(bound));
     return true;
   }
+  if (id == "int_abs" &&
+      !ContainsKey(stored_constraints_, index) &&
+      spec->Arg(0)->isIntVar() &&
+      spec->Arg(1)->isIntVar()) {
+    abs_map_[spec->Arg(1)->getIntVar()] = spec->Arg(0)->getIntVar();
+    stored_constraints_.insert(index);
+    return true;
+  }
+  if (id == "int_eq_reif") {
+    if (spec->Arg(0)->isIntVar() &&
+        ContainsKey(abs_map_, spec->Arg(0)->getIntVar()) &&
+        spec->Arg(1)->isInt() &&
+        spec->Arg(1)->getInt() == 0) {
+      VLOG(1) << "  - presolve:  remove abs() in " << spec->DebugString();
+      dynamic_cast<AST::IntVar*>(spec->Arg(0))->i =
+          abs_map_[spec->Arg(0)->getIntVar()];
+    }
+  }
+  if (id == "int_ne_reif") {
+    if (spec->Arg(0)->isIntVar() &&
+        ContainsKey(abs_map_, spec->Arg(0)->getIntVar()) &&
+        spec->Arg(1)->isInt() &&
+        spec->Arg(1)->getInt() == 0) {
+      VLOG(1) << "  - presolve:  remove abs() in " << spec->DebugString();
+      dynamic_cast<AST::IntVar*>(spec->Arg(0))->i =
+          abs_map_[spec->Arg(0)->getIntVar()];
+    }
+  }
+  if (id == "int_ne") {
+    if (spec->Arg(0)->isIntVar() &&
+        ContainsKey(abs_map_, spec->Arg(0)->getIntVar()) &&
+        spec->Arg(1)->isInt() &&
+        spec->Arg(1)->getInt() == 0) {
+      VLOG(1) << "  - presolve:  remove abs() in " << spec->DebugString();
+      dynamic_cast<AST::IntVar*>(spec->Arg(0))->i =
+          abs_map_[spec->Arg(0)->getIntVar()];
+    }
+  }
   return false;
 }
 
diff --git a/src/flatzinc/parser.h b/src/flatzinc/parser.h
index 229084d383..82fdb3283d 100644
--- a/src/flatzinc/parser.h
+++ b/src/flatzinc/parser.h
@@ -205,6 +205,8 @@ class ParserState {
   hash_map<string, std::vector<int> > constraints_per_id_;
   std::vector<std::vector<int> > constraints_per_int_variables_;
   std::vector<std::vector<int> > constraints_per_bool_variables_;
+  hash_map<int, int> abs_map_;
+  hash_map<int, std::pair<int, int> > differences_;
 };
 
 AST::Node* ArrayOutput(AST::Call* ann);