diff --git a/rego/rego.go b/rego/rego.go
index 4d82bab3c8..f6edcafa29 100644
--- a/rego/rego.go
+++ b/rego/rego.go
@@ -2147,9 +2147,10 @@ func (r *Rego) partial(ctx context.Context, ectx *EvalContext) (*PartialQueries,
 
 	var unknowns []*ast.Term
 
-	if ectx.parsedUnknowns != nil {
+	switch {
+	case ectx.parsedUnknowns != nil:
 		unknowns = ectx.parsedUnknowns
-	} else if ectx.unknowns != nil {
+	case ectx.unknowns != nil:
 		unknowns = make([]*ast.Term, len(ectx.unknowns))
 		for i := range ectx.unknowns {
 			var err error
@@ -2158,7 +2159,7 @@ func (r *Rego) partial(ctx context.Context, ectx *EvalContext) (*PartialQueries,
 				return nil, err
 			}
 		}
-	} else {
+	default:
 		// Use input document as unknown if caller has not specified any.
 		unknowns = []*ast.Term{ast.NewTerm(ast.InputRootRef)}
 	}
diff --git a/topdown/copypropagation/copypropagation.go b/topdown/copypropagation/copypropagation.go
index debae03dda..daf3bac4df 100644
--- a/topdown/copypropagation/copypropagation.go
+++ b/topdown/copypropagation/copypropagation.go
@@ -5,6 +5,7 @@
 package copypropagation
 
 import (
+	"fmt"
 	"sort"
 
 	"github.com/open-policy-agent/opa/ast"
@@ -31,6 +32,18 @@ type CopyPropagator struct {
 	sorted             []ast.Var  // sorted copy of vars to ensure deterministic result
 	ensureNonEmptyBody bool
 	compiler           *ast.Compiler
+	localvargen        *localVarGenerator
+}
+
+type localVarGenerator struct {
+	next int
+}
+
+func (l *localVarGenerator) Generate() ast.Var {
+	result := ast.Var(fmt.Sprintf("__localcp%d__", l.next))
+	l.next++
+	return result
+
 }
 
 // New returns a new CopyPropagator that optimizes queries while preserving vars
@@ -46,7 +59,7 @@ func New(livevars ast.VarSet) *CopyPropagator {
 		return sorted[i].Compare(sorted[j]) < 0
 	})
 
-	return &CopyPropagator{livevars: livevars, sorted: sorted}
+	return &CopyPropagator{livevars: livevars, sorted: sorted, localvargen: &localVarGenerator{}}
 }
 
 // WithEnsureNonEmptyBody configures p to ensure that results are always non-empty.
@@ -282,12 +295,16 @@ func (t bindingPlugTransform) plugBindingsRef(pctx *plugContext, v ast.Ref) ast.
 // updateBindings returns false if the expression can be killed. If the
 // expression is killed, the binding list is updated to map a var to value.
 func (p *CopyPropagator) updateBindings(pctx *plugContext, expr *ast.Expr) bool {
-	if pctx.negated || len(expr.With) > 0 {
+	switch {
+	case pctx.negated || len(expr.With) > 0:
 		return true
-	}
-	if expr.IsEquality() {
+
+	case expr.IsEquality():
 		a, b := expr.Operand(0), expr.Operand(1)
 		if a.Equal(b) {
+			if p.livevarRef(a) {
+				pctx.removedEqs.Put(p.localvargen.Generate(), a.Value)
+			}
 			return false
 		}
 		k, v, keep := p.updateBindingsEq(a, b)
@@ -297,7 +314,8 @@ func (p *CopyPropagator) updateBindings(pctx *plugContext, expr *ast.Expr) bool
 			}
 			return false
 		}
-	} else if expr.IsCall() {
+
+	case expr.IsCall():
 		terms := expr.Terms.([]*ast.Term)
 		if p.compiler.GetArity(expr.Operator()) == len(terms)-2 { // with captured output
 			output := terms[len(terms)-1]
@@ -310,6 +328,21 @@ func (p *CopyPropagator) updateBindings(pctx *plugContext, expr *ast.Expr) bool
 	return !isNoop(expr)
 }
 
+func (p *CopyPropagator) livevarRef(a *ast.Term) bool {
+	ref, ok := a.Value.(ast.Ref)
+	if !ok {
+		return false
+	}
+
+	for _, v := range p.sorted {
+		if ref[0].Value.Compare(v) == 0 {
+			return true
+		}
+	}
+
+	return false
+}
+
 func (p *CopyPropagator) updateBindingsEq(a, b *ast.Term) (ast.Var, ast.Value, bool) {
 	k, v, keep := p.updateBindingsEqAsymmetric(a, b)
 	if !keep {
@@ -340,8 +373,7 @@ type plugContext struct {
 }
 
 type binding struct {
-	k ast.Value
-	v ast.Value
+	k, v ast.Value
 }
 
 func containedIn(value ast.Value, x interface{}) bool {
@@ -374,7 +406,7 @@ func sortbindings(bindings *ast.ValueMap) []*binding {
 		return false
 	})
 	sort.Slice(sorted, func(i, j int) bool {
-		return sorted[i].k.Compare(sorted[j].k) < 0
+		return sorted[i].k.Compare(sorted[j].k) > 0
 	})
 	return sorted
 }
@@ -397,17 +429,21 @@ func makeDisjointSets(livevars ast.VarSet, query ast.Body) (*unionFind, bool) {
 			a, b := expr.Operand(0), expr.Operand(1)
 			varA, ok1 := a.Value.(ast.Var)
 			varB, ok2 := b.Value.(ast.Var)
-			if ok1 && ok2 {
+
+			switch {
+			case ok1 && ok2:
 				if _, ok := uf.Merge(varA, varB); !ok {
 					return nil, false
 				}
-			} else if ok1 && ast.IsConstant(b.Value) {
+
+			case ok1 && ast.IsConstant(b.Value):
 				root := uf.MakeSet(varA)
 				if root.constant != nil && !root.constant.Equal(b) {
 					return nil, false
 				}
 				root.constant = b
-			} else if ok2 && ast.IsConstant(a.Value) {
+
+			case ok2 && ast.IsConstant(a.Value):
 				root := uf.MakeSet(varB)
 				if root.constant != nil && !root.constant.Equal(a) {
 					return nil, false
diff --git a/topdown/query.go b/topdown/query.go
index 93f2ee3fe2..544c752e86 100644
--- a/topdown/query.go
+++ b/topdown/query.go
@@ -340,6 +340,14 @@ func (q *Query) PartialRun(ctx context.Context) (partials []ast.Body, support []
 	defer q.metrics.Timer(metrics.RegoPartialEval).Stop()
 
 	livevars := ast.NewVarSet()
+	for _, t := range q.unknowns {
+		switch v := t.Value.(type) {
+		case ast.Var:
+			livevars.Add(v)
+		case ast.Ref:
+			livevars.Add(v[0].Value.(ast.Var))
+		}
+	}
 
 	ast.WalkVars(q.query, func(x ast.Var) bool {
 		if !x.IsGenerated() {
diff --git a/topdown/topdown_partial_test.go b/topdown/topdown_partial_test.go
index bef79be8a9..435cf00e10 100644
--- a/topdown/topdown_partial_test.go
+++ b/topdown/topdown_partial_test.go
@@ -1826,6 +1826,100 @@ func TestTopDownPartialEval(t *testing.T) {
 				),
 			},
 		},
+		{
+			note:  "copy propagation: circular reference (bug 3559)",
+			query: "data.test.p",
+			modules: []string{`package test
+				p {
+					q[_]
+				}
+				q[x] {
+					x = input[x]
+				}`,
+			},
+			wantQueries: []string{`x_term_1_01; x_term_1_01 = input[x_term_1_01]`},
+		},
+		{
+			note:  "copy propagation: circular reference (bug 3071)",
+			query: "data.test.p",
+			modules: []string{`package test
+				p[y] {
+					s := { i | input[i] }
+					s & set() != s
+					y := sprintf("%v", [s])
+				}`,
+			},
+			wantQueries: []string{`data.partial.test.p`},
+			wantSupport: []string{`package partial.test
+				p[__local1__1] { __local0__1 = {i1 | input[i1]}; neq(and(__local0__1, set()), __local0__1); sprintf("%v", [__local0__1], __local1__1) }
+			`},
+		},
+		{
+			note:        "copy propagation: tautology in query, input ref",
+			query:       "input.a == input.a",
+			wantQueries: []string{`__localq1__ = input.a`},
+		},
+		{
+			note:        "copy propagation: tautology in query, var ref, var is input",
+			query:       "x := input; x.a == x.a",
+			wantQueries: []string{`__localq2__ = input.a`},
+		},
+		{
+			note:  "copy propagation: tautology, input ref",
+			query: "data.test.p",
+			modules: []string{`package test
+				p {
+					input.a == input.a
+				}`,
+			},
+			wantQueries: []string{`__localcp0__ = input.a`},
+		},
+		{
+			note:  "copy propagation: tautology, var ref, ref is input",
+			query: "data.test.p",
+			modules: []string{`package test
+				p {
+					x := input
+					x.a == x.a
+				}`,
+			},
+			wantQueries: []string{`__localcp0__ = input.a`},
+		},
+		{
+			note:     "copy propagation: tautology, var ref, ref is unknown data",
+			query:    "data.test.p",
+			unknowns: []string{"data.bar.foo"},
+			modules: []string{`package test
+				p {
+					data.bar.foo.a == data.bar.foo.a
+				}`,
+			},
+			wantQueries: []string{`__localcp0__ = data.bar.foo.a`},
+		},
+		{
+			note: "copy propagation: tautology, var ref, ref is input, via unknown",
+			// NOTE(sr): If we were having unkowns: [input.foo] and the rule body was
+			// input.a == input.a, we'd never reach copy-propagation -- partial eval would
+			// have failed before.
+			query:    "data.test.p",
+			unknowns: []string{"input"},
+			modules: []string{`package test
+				p {
+					input.foo.a == input.foo.a
+				}`,
+			},
+			wantQueries: []string{`__localcp0__ = input.foo.a`},
+		},
+		{
+			note:  "copy propagation: tautology, var ref, ref is head var",
+			query: "data.test.p(input)",
+			modules: []string{`package test
+				p(x) {
+					x.a == x.a
+				}`,
+			},
+			wantQueries: []string{`__localcp1__ = input.a`},
+		},
 		{
 			note:  "save set vars are namespaced",
 			query: "input = x; data.test.f(1)",
@@ -2985,7 +3079,12 @@ func TestTopDownPartialEval(t *testing.T) {
 					x = true
 				}`,
 			},
-			wantQueries: []string{"a1 = input.foo1; b1 = input.foo2; c1 = input.foo3; d1 = input.foo4; e1 = input.foo5"},
+			wantQueries: []string{`
+				e1 = input.foo5
+				d1 = input.foo4
+				c1 = input.foo3
+				b1 = input.foo2
+				a1 = input.foo1`},
 		},
 		{
 			note:  "partial object rules not memoized",
@@ -3054,34 +3153,6 @@ func TestTopDownPartialEval(t *testing.T) {
 			shallow:              true,
 			skipPartialNamespace: true,
 		},
-		{
-			note:  "copypropagation: circular reference (bug 3559)",
-			query: "data.test.p",
-			modules: []string{`package test
-				p {
-					q[_]
-				}
-				q[x] {
-					x = input[x]
-				}`,
-			},
-			wantQueries: []string{`x_term_1_01; x_term_1_01 = input[x_term_1_01]`},
-		},
-		{
-			note:  "copypropagation: circular reference (bug 3071)",
-			query: "data.test.p",
-			modules: []string{`package test
-				p[y] {
-					s := { i | input[i] }
-					s & set() != s
-					y := sprintf("%v", [s])
-				}`,
-			},
-			wantQueries: []string{`data.partial.test.p`},
-			wantSupport: []string{`package partial.test
-				p[__local1__1] { __local0__1 = {i1 | input[i1]}; neq(and(__local0__1, set()), __local0__1); sprintf("%v", [__local0__1], __local1__1) }
-			`},
-		},
 		{
 			note:  "every: empty domain, no unknowns",
 			query: "data.test.p",