diff --git a/frontend/cs/r1cs/api_assertions.go b/frontend/cs/r1cs/api_assertions.go
index b75f200f7a..530a5fe412 100644
--- a/frontend/cs/r1cs/api_assertions.go
+++ b/frontend/cs/r1cs/api_assertions.go
@@ -28,6 +28,15 @@ import (
 
 // AssertIsEqual adds an assertion in the constraint builder (i1 == i2)
 func (builder *builder) AssertIsEqual(i1, i2 frontend.Variable) {
+	c1, i1Constant := builder.constantValue(i1)
+	c2, i2Constant := builder.constantValue(i2)
+
+	if i1Constant && i2Constant {
+		if c1 != c2 {
+			panic("non-equal constant values")
+		}
+		return
+	}
 	// encoded 1 * i1 == i2
 	r := builder.getLinearExpression(builder.toVariable(i1))
 	o := builder.getLinearExpression(builder.toVariable(i2))
diff --git a/frontend/cs/r1cs/builder.go b/frontend/cs/r1cs/builder.go
index df1306b4c4..a070a6c7ad 100644
--- a/frontend/cs/r1cs/builder.go
+++ b/frontend/cs/r1cs/builder.go
@@ -308,6 +308,9 @@ func (builder *builder) constantValue(v frontend.Variable) (constraint.Element,
 			// and are always reduced to one element. may not always be true?
 			return constraint.Element{}, false
 		}
+		if _v[0].Coeff.IsZero() {
+			return constraint.Element{}, true
+		}
 		if !(_v[0].WireID() == 0) { // public ONE WIRE
 			return constraint.Element{}, false
 		}
diff --git a/frontend/cs/r1cs/r1cs_test.go b/frontend/cs/r1cs/r1cs_test.go
index ceb965322c..02762db1e0 100644
--- a/frontend/cs/r1cs/r1cs_test.go
+++ b/frontend/cs/r1cs/r1cs_test.go
@@ -160,3 +160,23 @@ func TestPreCompileHook(t *testing.T) {
 		t.Error("callback not called")
 	}
 }
+
+type subSameNoConstraintCircuit struct {
+	A frontend.Variable
+}
+
+func (c *subSameNoConstraintCircuit) Define(api frontend.API) error {
+	r := api.Sub(c.A, c.A)
+	api.AssertIsEqual(r, 0)
+	return nil
+}
+
+func TestSubSameNoConstraint(t *testing.T) {
+	ccs, err := frontend.Compile(ecc.BN254.ScalarField(), NewBuilder, &subSameNoConstraintCircuit{})
+	if err != nil {
+		t.Fatal(err)
+	}
+	if ccs.GetNbConstraints() != 0 {
+		t.Fatal("expected 0 constraints")
+	}
+}
diff --git a/frontend/cs/scs/api_test.go b/frontend/cs/scs/api_test.go
index 40c967203d..1f81e31c15 100644
--- a/frontend/cs/scs/api_test.go
+++ b/frontend/cs/scs/api_test.go
@@ -238,3 +238,22 @@ func TestMulAccFastTrack(t *testing.T) {
 	assert.NoError(err)
 	_ = solution
 }
+
+type subSameNoConstraintCircuit struct {
+	A frontend.Variable
+}
+
+func (c *subSameNoConstraintCircuit) Define(api frontend.API) error {
+	r := api.Sub(c.A, c.A)
+	api.AssertIsEqual(r, 0)
+	return nil
+}
+
+func TestSubSameNoConstraint(t *testing.T) {
+	assert := test.NewAssert(t)
+	ccs, err := frontend.Compile(ecc.BN254.ScalarField(), scs.NewBuilder, &subSameNoConstraintCircuit{})
+	assert.NoError(err)
+	if ccs.GetNbConstraints() != 0 {
+		t.Fatal("expected 0 constraints")
+	}
+}
diff --git a/frontend/cs/scs/builder.go b/frontend/cs/scs/builder.go
index 16a9ddd289..0ca3666fac 100644
--- a/frontend/cs/scs/builder.go
+++ b/frontend/cs/scs/builder.go
@@ -17,6 +17,7 @@ limitations under the License.
 package scs
 
 import (
+	"fmt"
 	"math/big"
 	"reflect"
 	"sort"
@@ -312,7 +313,10 @@ func (builder *builder) ConstantValue(v frontend.Variable) (*big.Int, bool) {
 }
 
 func (builder *builder) constantValue(v frontend.Variable) (constraint.Element, bool) {
-	if _, ok := v.(expr.Term); ok {
+	if vv, ok := v.(expr.Term); ok {
+		if vv.Coeff.IsZero() {
+			return constraint.Element{}, true
+		}
 		return constraint.Element{}, false
 	}
 	return builder.cs.FromInterface(v), true
@@ -686,3 +690,63 @@ func (builder *builder) ToCanonicalVariable(v frontend.Variable) frontend.Canoni
 		return term
 	}
 }
+
+// GetWireConstraints returns the pairs (constraintID, wireLocation) for the
+// given wires in the compiled constraint system:
+//   - constraintID is the index of the constraint in the constraint system.
+//   - wireLocation is the location of the wire in the constraint (0=xA or 1=xB).
+//
+// If the argument addMissing is true, then the function will add a new
+// constraint for each wire that is not found in the constraint system. This may
+// happen when getting the constraint for a witness which is not used in
+// constraints. Otherwise, when addMissing is false, the function returns an
+// error if a wire is not found in the constraint system.
+//
+// The method only returns a single pair (constraintID, wireLocation) for every
+// unique wire (removing duplicates). The order of the returned pairs is not the
+// same as for the given arguments.
+func (builder *builder) GetWireConstraints(wires []frontend.Variable, addMissing bool) ([][2]int, error) {
+	// construct a lookup table table for later quick access when iterating over instructions
+	lookup := make(map[int]struct{})
+	for _, w := range wires {
+		ww, ok := w.(expr.Term)
+		if !ok {
+			panic("input wire is not a Term")
+		}
+		lookup[ww.WireID()] = struct{}{}
+	}
+	res := make([][2]int, 0, len(wires))
+	iterator := builder.cs.GetSparseR1CIterator()
+	for c, constraintIdx := iterator.Next(), 0; c != nil; c, constraintIdx = iterator.Next(), constraintIdx+1 {
+		if _, ok := lookup[int(c.XA)]; ok {
+			res = append(res, [2]int{constraintIdx, 0})
+			delete(lookup, int(c.XA))
+			continue
+		}
+		if _, ok := lookup[int(c.XB)]; ok {
+			res = append(res, [2]int{constraintIdx, 1})
+			delete(lookup, int(c.XB))
+			continue
+		}
+	}
+	if addMissing {
+		nbWitnessWires := builder.cs.GetNbPublicVariables() + builder.cs.GetNbSecretVariables()
+		for k := range lookup {
+			if k >= nbWitnessWires {
+				return nil, fmt.Errorf("addMissing is true, but wire %d is not a witness", k)
+			}
+			constraintIdx := builder.cs.AddSparseR1C(constraint.SparseR1C{
+				XA: uint32(k),
+				XC: uint32(k),
+				QL: constraint.CoeffIdOne,
+				QO: constraint.CoeffIdMinusOne,
+			}, builder.genericGate)
+			res = append(res, [2]int{constraintIdx, 0})
+			delete(lookup, k)
+		}
+	}
+	if len(lookup) > 0 {
+		return nil, fmt.Errorf("constraint with wire not found in circuit")
+	}
+	return res, nil
+}