diff --git a/dnssec.go b/dnssec.go
index 1be87eae6..ffdafcebd 100644
--- a/dnssec.go
+++ b/dnssec.go
@@ -250,14 +250,6 @@ func (d *DS) ToCDS() *CDS {
 // zero, it is used as-is, otherwise the TTL of the RRset is used as the
 // OrigTTL.
 func (rr *RRSIG) Sign(k crypto.Signer, rrset []RR) error {
-	if k == nil {
-		return ErrPrivKey
-	}
-	// s.Inception and s.Expiration may be 0 (rollover etc.), the rest must be set
-	if rr.KeyTag == 0 || len(rr.SignerName) == 0 || rr.Algorithm == 0 {
-		return ErrKey
-	}
-
 	h0 := rrset[0].Header()
 	rr.Hdr.Rrtype = TypeRRSIG
 	rr.Hdr.Name = h0.Name
@@ -272,6 +264,18 @@ func (rr *RRSIG) Sign(k crypto.Signer, rrset []RR) error {
 		rr.Labels-- // wildcard, remove from label count
 	}
 
+	return rr.signAsIs(k, rrset)
+}
+
+func (rr *RRSIG) signAsIs(k crypto.Signer, rrset []RR) error {
+	if k == nil {
+		return ErrPrivKey
+	}
+	// s.Inception and s.Expiration may be 0 (rollover etc.), the rest must be set
+	if rr.KeyTag == 0 || len(rr.SignerName) == 0 || rr.Algorithm == 0 {
+		return ErrKey
+	}
+
 	sigwire := new(rrsigWireFmt)
 	sigwire.TypeCovered = rr.TypeCovered
 	sigwire.Algorithm = rr.Algorithm
@@ -370,9 +374,12 @@ func (rr *RRSIG) Verify(k *DNSKEY, rrset []RR) error {
 	if rr.Algorithm != k.Algorithm {
 		return ErrKey
 	}
-	if !strings.EqualFold(rr.SignerName, k.Hdr.Name) {
+
+	signerName := CanonicalName(rr.SignerName)
+	if !equal(signerName, k.Hdr.Name) {
 		return ErrKey
 	}
+
 	if k.Protocol != 3 {
 		return ErrKey
 	}
@@ -384,9 +391,18 @@ func (rr *RRSIG) Verify(k *DNSKEY, rrset []RR) error {
 	}
 
 	// IsRRset checked that we have at least one RR and that the RRs in
-	// the set have consistent type, class, and name. Also check that type and
-	// class matches the RRSIG record.
-	if h0 := rrset[0].Header(); h0.Class != rr.Hdr.Class || h0.Rrtype != rr.TypeCovered {
+	// the set have consistent type, class, and name. Also check that type,
+	// class and name matches the RRSIG record.
+	// Also checks RFC 4035 5.3.1 the number of labels in the RRset owner
+	// name MUST be greater than or equal to the value in the RRSIG RR's Labels field.
+	// RFC 4035 5.3.1 Signer's Name MUST be the name of the zone that [contains the RRset].
+	// Since we don't have SOA info, checking suffix may be the best we can do...?
+	if h0 := rrset[0].Header(); h0.Class != rr.Hdr.Class ||
+		h0.Rrtype != rr.TypeCovered ||
+		uint8(CountLabel(h0.Name)) < rr.Labels ||
+		!equal(h0.Name, rr.Hdr.Name) ||
+		!strings.HasSuffix(CanonicalName(h0.Name), signerName) {
+
 		return ErrRRset
 	}
 
@@ -400,7 +416,7 @@ func (rr *RRSIG) Verify(k *DNSKEY, rrset []RR) error {
 	sigwire.Expiration = rr.Expiration
 	sigwire.Inception = rr.Inception
 	sigwire.KeyTag = rr.KeyTag
-	sigwire.SignerName = CanonicalName(rr.SignerName)
+	sigwire.SignerName = signerName
 	// Create the desired binary blob
 	signeddata := make([]byte, DefaultMsgSize)
 	n, err := packSigWire(sigwire, signeddata)
diff --git a/dnssec_test.go b/dnssec_test.go
index 1511278c0..4f04e85f6 100644
--- a/dnssec_test.go
+++ b/dnssec_test.go
@@ -155,6 +155,117 @@ func TestSignVerify(t *testing.T) {
 	}
 }
 
+// Test if RRSIG.Verify() conforms to RFC 4035 Section 5.3.1
+func TestShouldNotVerifyInvalidSig(t *testing.T) {
+	// The RRSIG RR and the RRset MUST have the same owner name
+	rrNameMismatch := getSoa()
+	rrNameMismatch.Hdr.Name = "example.com."
+
+	// ... and the same class
+	rrClassMismatch := getSoa()
+	rrClassMismatch.Hdr.Class = ClassCHAOS
+
+	// The RRSIG RR's Type Covered field MUST equal the RRset's type.
+	rrTypeMismatch := getSoa()
+	rrTypeMismatch.Hdr.Rrtype = TypeA
+
+	// The number of labels in the RRset owner name MUST be greater than
+	// or equal to the value in the RRSIG RR's Labels field.
+	rrLabelLessThan := getSoa()
+	rrLabelLessThan.Hdr.Name = "nl."
+
+	// Time checks are done in ValidityPeriod
+
+	// With this key
+	key := new(DNSKEY)
+	key.Hdr.Rrtype = TypeDNSKEY
+	key.Hdr.Name = "miek.nl."
+	key.Hdr.Class = ClassINET
+	key.Hdr.Ttl = 14400
+	key.Flags = 256
+	key.Protocol = 3
+	key.Algorithm = RSASHA256
+	privkey, _ := key.Generate(512)
+
+	normalSoa := getSoa()
+
+	// Fill in the normal values of the Sig, before signing
+	sig := new(RRSIG)
+	sig.Hdr = RR_Header{"miek.nl.", TypeRRSIG, ClassINET, 14400, 0}
+	sig.TypeCovered = TypeSOA
+	sig.Labels = uint8(CountLabel(normalSoa.Hdr.Name))
+	sig.OrigTtl = normalSoa.Hdr.Ttl
+	sig.Expiration = 1296534305 // date -u '+%s' -d"2011-02-01 04:25:05"
+	sig.Inception = 1293942305  // date -u '+%s' -d"2011-01-02 04:25:05"
+	sig.KeyTag = key.KeyTag()   // Get the keyfrom the Key
+	sig.SignerName = key.Hdr.Name
+	sig.Algorithm = RSASHA256
+
+	for i, rr := range []RR{rrNameMismatch, rrClassMismatch, rrTypeMismatch, rrLabelLessThan} {
+		if i != 0 { // Just for the rrNameMismatch case, we need the name to mismatch
+			sig := sig.copy().(*RRSIG)
+			sig.SignerName = rr.Header().Name
+			sig.Hdr.Name = rr.Header().Name
+			key := key.copy().(*DNSKEY)
+			key.Hdr.Name = rr.Header().Name
+		}
+
+		if err := sig.signAsIs(privkey.(*rsa.PrivateKey), []RR{rr}); err != nil {
+			t.Error("failure to sign the record:", err)
+			continue
+		}
+
+		if err := sig.Verify(key, []RR{rr}); err == nil {
+			t.Error("should not validate: ", rr)
+			continue
+		} else {
+			t.Logf("expected failure: %v for RR name %s, class %d, type %d, rrsig labels %d", err, rr.Header().Name, rr.Header().Class, rr.Header().Rrtype, CountLabel(rr.Header().Name))
+		}
+	}
+
+	// The RRSIG RR's Signer's Name field MUST be the name of the zone that contains the RRset.
+	// The RRSIG RR's Signer's Name, Algorithm, and Key Tag fields MUST match the owner name,
+	// algorithm, and key tag for some DNSKEY RR in the zone's apex DNSKEY RRset.
+	sigMismatchName := sig.copy().(*RRSIG)
+	sigMismatchName.SignerName = "example.com."
+	soaMismatchName := getSoa()
+	soaMismatchName.Hdr.Name = "example.com."
+	keyMismatchName := key.copy().(*DNSKEY)
+	keyMismatchName.Hdr.Name = "example.com."
+	if err := sigMismatchName.signAsIs(privkey.(*rsa.PrivateKey), []RR{soaMismatchName}); err != nil {
+		t.Error("failure to sign the record:", err)
+	} else if err := sigMismatchName.Verify(keyMismatchName, []RR{soaMismatchName}); err == nil {
+		t.Error("should not validate: ", soaMismatchName, ", RRSIG's signer's name does not match the owner name")
+	} else {
+		t.Logf("expected failure: %v for signer %s and owner %s", err, sigMismatchName.SignerName, sigMismatchName.Hdr.Name)
+	}
+
+	sigMismatchAlgo := sig.copy().(*RRSIG)
+	sigMismatchAlgo.Algorithm = RSASHA1
+	sigMismatchKeyTag := sig.copy().(*RRSIG)
+	sigMismatchKeyTag.KeyTag = 12345
+	for _, sigMismatch := range []*RRSIG{sigMismatchAlgo, sigMismatchKeyTag} {
+		if err := sigMismatch.Sign(privkey.(*rsa.PrivateKey), []RR{normalSoa}); err != nil {
+			t.Error("failure to sign the record:", err)
+		} else if err := sigMismatch.Verify(key, []RR{normalSoa}); err == nil {
+			t.Error("should not validate: ", normalSoa)
+		} else {
+			t.Logf("expected failure: %v for signer %s algo %d keytag %d", err, sigMismatch.SignerName, sigMismatch.Algorithm, sigMismatch.KeyTag)
+		}
+	}
+
+	// The matching DNSKEY RR MUST have the Zone Flag bit (DNSKEY RDATA Flag bit 7) set.
+	keyZoneBitWrong := key.copy().(*DNSKEY)
+	keyZoneBitWrong.Flags = key.Flags &^ ZONE
+	if err := sig.Sign(privkey.(*rsa.PrivateKey), []RR{normalSoa}); err != nil {
+		t.Error("failure to sign the record:", err)
+	} else if err := sig.Verify(keyZoneBitWrong, []RR{normalSoa}); err == nil {
+		t.Error("should not validate: ", normalSoa)
+	} else {
+		t.Logf("expected failure: %v for key flags %d", err, keyZoneBitWrong.Flags)
+	}
+}
+
 func Test65534(t *testing.T) {
 	t6 := new(RFC3597)
 	t6.Hdr = RR_Header{"miek.nl.", 65534, ClassINET, 14400, 0}
diff --git a/sig0.go b/sig0.go
index 2c4b10352..057bb5787 100644
--- a/sig0.go
+++ b/sig0.go
@@ -7,7 +7,6 @@ import (
 	"crypto/rsa"
 	"encoding/binary"
 	"math/big"
-	"strings"
 	"time"
 )
 
@@ -151,7 +150,7 @@ func (rr *SIG) Verify(k *KEY, buf []byte) error {
 	}
 	// If key has come from the DNS name compression might
 	// have mangled the case of the name
-	if !strings.EqualFold(signername, k.Header().Name) {
+	if !equal(signername, k.Header().Name) {
 		return &Error{err: "signer name doesn't match key name"}
 	}
 	sigend := offset