diff --git a/pkg/air/expr.go b/pkg/air/expr.go
index ea55083..cbbb691 100644
--- a/pkg/air/expr.go
+++ b/pkg/air/expr.go
@@ -28,6 +28,11 @@ type Expr interface {
 
 	// Equate one expression with another
 	Equate(Expr) Expr
+
+	// AsConstant determines whether or not this is a constant expression.  If
+	// so, the constant is returned; otherwise, nil is returned.  NOTE: this
+	// does not perform any form of simplification to determine this.
+	AsConstant() *fr.Element
 }
 
 // ============================================================================
@@ -77,6 +82,11 @@ func (p *Add) Equate(other Expr) Expr { return &Sub{Args: []Expr{p, other}} }
 // direction (right).
 func (p *Add) Bounds() util.Bounds { return util.BoundsForArray(p.Args) }
 
+// AsConstant determines whether or not this is a constant expression.  If
+// so, the constant is returned; otherwise, nil is returned.  NOTE: this
+// does not perform any form of simplification to determine this.
+func (p *Add) AsConstant() *fr.Element { return nil }
+
 // ============================================================================
 // Subtraction
 // ============================================================================
@@ -124,6 +134,11 @@ func (p *Sub) Equate(other Expr) Expr { return &Sub{Args: []Expr{p, other}} }
 // direction (right).
 func (p *Sub) Bounds() util.Bounds { return util.BoundsForArray(p.Args) }
 
+// AsConstant determines whether or not this is a constant expression.  If
+// so, the constant is returned; otherwise, nil is returned.  NOTE: this
+// does not perform any form of simplification to determine this.
+func (p *Sub) AsConstant() *fr.Element { return nil }
+
 // ============================================================================
 // Multiplication
 // ============================================================================
@@ -171,6 +186,11 @@ func (p *Mul) Equate(other Expr) Expr { return &Sub{Args: []Expr{p, other}} }
 // direction (right).
 func (p *Mul) Bounds() util.Bounds { return util.BoundsForArray(p.Args) }
 
+// AsConstant determines whether or not this is a constant expression.  If
+// so, the constant is returned; otherwise, nil is returned.  NOTE: this
+// does not perform any form of simplification to determine this.
+func (p *Mul) AsConstant() *fr.Element { return nil }
+
 // ============================================================================
 // Constant
 // ============================================================================
@@ -225,6 +245,11 @@ func (p *Constant) Equate(other Expr) Expr { return &Sub{Args: []Expr{p, other}}
 // direction (right).  A constant has zero shift.
 func (p *Constant) Bounds() util.Bounds { return util.EMPTY_BOUND }
 
+// AsConstant determines whether or not this is a constant expression.  If
+// so, the constant is returned; otherwise, nil is returned.  NOTE: this
+// does not perform any form of simplification to determine this.
+func (p *Constant) AsConstant() *fr.Element { return &p.Value }
+
 // ColumnAccess represents reading the value held at a given column in the
 // tabular context.  Furthermore, the current row maybe shifted up (or down) by
 // a given amount. Suppose we are evaluating a constraint on row k=5 which
@@ -290,3 +315,8 @@ func (p *ColumnAccess) Bounds() util.Bounds {
 	// Negative shift
 	return util.NewBounds(uint(-p.Shift), 0)
 }
+
+// AsConstant determines whether or not this is a constant expression.  If
+// so, the constant is returned; otherwise, nil is returned.  NOTE: this
+// does not perform any form of simplification to determine this.
+func (p *ColumnAccess) AsConstant() *fr.Element { return nil }
diff --git a/pkg/mir/const.go b/pkg/mir/const.go
index 1dcf0a0..b5854cd 100644
--- a/pkg/mir/const.go
+++ b/pkg/mir/const.go
@@ -88,6 +88,7 @@ func applyConstantPropagationMul(es []Expr, schema sc.Schema) Expr {
 	is_const := true
 	prod := one
 	rs := make([]Expr, len(es))
+	ones := 0
 	//
 	for i, e := range es {
 		rs[i] = applyConstantPropagation(e, schema)
@@ -97,6 +98,9 @@ func applyConstantPropagationMul(es []Expr, schema sc.Schema) Expr {
 		if ok && c.Value.IsZero() {
 			// No matter what, outcome is zero.
 			return &Constant{c.Value}
+		} else if ok && c.Value.IsOne() {
+			ones++
+			rs[i] = nil
 		} else if ok && is_const {
 			// Continue building constant
 			prod.Mul(&prod, &c.Value)
@@ -107,8 +111,14 @@ func applyConstantPropagationMul(es []Expr, schema sc.Schema) Expr {
 	// Check if constant
 	if is_const {
 		return &Constant{prod}
+	} else if ones > 0 {
+		rs = util.RemoveMatching[Expr](rs, func(item Expr) bool { return item == nil })
 	}
-	//
+	// Sanity check what's left.
+	if len(rs) == 1 {
+		return rs[0]
+	}
+	// Done
 	return &Mul{rs}
 }
 
diff --git a/pkg/mir/lower.go b/pkg/mir/lower.go
index 646039e..07a6a87 100644
--- a/pkg/mir/lower.go
+++ b/pkg/mir/lower.go
@@ -63,7 +63,14 @@ func lowerConstraintToAir(c sc.Constraint, schema *air.Schema) {
 		lowerLookupConstraintToAir(v, schema)
 	} else if v, ok := c.(VanishingConstraint); ok {
 		air_expr := lowerExprTo(v.Context(), v.Constraint().Expr, schema)
-		schema.AddVanishingConstraint(v.Handle(), v.Context(), v.Domain(), air_expr)
+		// Check whether this is a constant
+		constant := air_expr.AsConstant()
+		// Check for compile-time constants
+		if constant != nil && !constant.IsZero() {
+			panic(fmt.Sprintf("constraint %s cannot vanish!", v.Handle()))
+		} else if constant == nil {
+			schema.AddVanishingConstraint(v.Handle(), v.Context(), v.Domain(), air_expr)
+		}
 	} else if v, ok := c.(*constraint.TypeConstraint); ok {
 		if t := v.Type().AsUint(); t != nil {
 			// Yes, a constraint is implied.  Now, decide whether to use a range
diff --git a/pkg/util/arrays.go b/pkg/util/arrays.go
index 0557c86..da8f683 100644
--- a/pkg/util/arrays.go
+++ b/pkg/util/arrays.go
@@ -21,6 +21,33 @@ func ReplaceFirstOrPanic[T comparable](columns []T, from T, to T) {
 	panic(fmt.Sprintf("invalid replace (item %s not found)", any(from)))
 }
 
+// RemoveMatching removes all elements from an array matching the given item.
+func RemoveMatching[T any](items []T, predicate Predicate[T]) []T {
+	count := 0
+	// Check how many matches we have
+	for _, r := range items {
+		if !predicate(r) {
+			count++
+		}
+	}
+	// Check for stuff to remove
+	if count != len(items) {
+		nitems := make([]T, count)
+		j := 0
+		// Remove items
+		for i, r := range items {
+			if !predicate(r) {
+				nitems[j] = items[i]
+				j++
+			}
+		}
+		//
+		items = nitems
+	}
+	//
+	return items
+}
+
 // Equals returns true if both arrays contain equivalent elements.
 func Equals(lhs []*fr.Element, rhs []*fr.Element) bool {
 	if len(lhs) != len(rhs) {