diff --git a/src/dtls.rs b/src/dtls.rs
index fdca601..6c1b1c1 100644
--- a/src/dtls.rs
+++ b/src/dtls.rs
@@ -113,6 +113,7 @@ pub enum DTLSMessageHandshakeBody<'a> {
     Finished(&'a [u8]),
     CertificateStatus(TlsCertificateStatusContents<'a>),
     NextProtocol(TlsNextProtocolContent<'a>),
+    Fragment(&'a [u8]),
 }
 
 /// DTLS plaintext message
@@ -127,6 +128,17 @@ pub enum DTLSMessage<'a> {
     Heartbeat(TlsMessageHeartbeat<'a>),
 }
 
+impl<'a> DTLSMessage<'a> {
+    /// Tell if this DTLSMessage is a (handshake) fragment that needs combining with other
+    /// fragments to be a complete message.
+    pub fn is_fragment(&self) -> bool {
+        match self {
+            DTLSMessage::Handshake(h) => matches!(h.body, DTLSMessageHandshakeBody::Fragment(_)),
+            _ => false,
+        }
+    }
+}
+
 // --------------------------- PARSERS ---------------------------
 
 /// DTLS record header
@@ -148,6 +160,11 @@ pub fn parse_dtls_record_header(i: &[u8]) -> IResult<&[u8], DTLSRecordHeader> {
     Ok((i, record))
 }
 
+/// Treat the entire input as an opaque fragment.
+fn parse_dtls_fragment(i: &[u8]) -> IResult<&[u8], DTLSMessageHandshakeBody> {
+    Ok((&[], DTLSMessageHandshakeBody::Fragment(i)))
+}
+
 /// DTLS Client Hello
 // Section 4.2 of RFC6347
 fn parse_dtls_client_hello(i: &[u8]) -> IResult<&[u8], DTLSMessageHandshakeBody> {
@@ -222,8 +239,16 @@ pub fn parse_dtls_message_handshake(i: &[u8]) -> IResult<&[u8], DTLSMessage> {
     let (i, message_seq) = be_u16(i)?;
     let (i, fragment_offset) = be_u24(i)?;
     let (i, fragment_length) = be_u24(i)?;
-    let (i, raw_msg) = take(length)(i)?;
+    // This packet contains fragment_length (which is less than length for fragmentation)
+    let (i, raw_msg) = take(fragment_length)(i)?;
+
+    // Handshake messages can be fragmented over multiple packets. When fragmented, the user
+    // needs the fragment_offset, fragment_length and length to determine whether they received
+    // all the fragments. The DTLS spec allows for overlapping and duplicated fragments.
+    let is_fragment = fragment_offset > 0 || fragment_length < length;
+
     let (_, body) = match msg_type {
+        _ if is_fragment => parse_dtls_fragment(raw_msg),
         TlsHandshakeType::ClientHello => parse_dtls_client_hello(raw_msg),
         TlsHandshakeType::HelloVerifyRequest => parse_dtls_hello_verify_request(raw_msg),
         TlsHandshakeType::ServerHello => parse_dtls_handshake_msg_server_hello_tlsv12(raw_msg),
@@ -281,18 +306,6 @@ pub fn parse_dtls_record_with_header<'i>(
     }
 }
 
-/// Parse DTLS record, leaving `fragment` unparsed
-// Section 4.1 of RFC6347
-pub fn parse_dtls_raw_record(i: &[u8]) -> IResult<&[u8], DTLSRawRecord> {
-    let (i, header) = parse_dtls_record_header(i)?;
-    // As in TLS 1.2, the length should not exceed 2^14.
-    if header.length > MAX_RECORD_LEN {
-        return Err(Err::Error(make_error(i, ErrorKind::TooLarge)));
-    }
-    let (i, fragment) = take(header.length as usize)(i)?;
-    Ok((i, DTLSRawRecord { header, fragment }))
-}
-
 /// Parse one DTLS plaintext record
 // Section 4.1 of RFC6347
 pub fn parse_dtls_plaintext_record(i: &[u8]) -> IResult<&[u8], DTLSPlaintext> {