diff --git a/internal/httpapi/mailbox_handlers.go b/internal/httpapi/mailbox_handlers.go
index 9b05b6a..8c1b135 100644
--- a/internal/httpapi/mailbox_handlers.go
+++ b/internal/httpapi/mailbox_handlers.go
@@ -147,7 +147,7 @@ func (s *Server) SyncMailbox(ctx context.Context, user *store.User, m *store.Mai
 	}
 	defer client.Close()
 
-	messages, err := client.Since(m.LastUID, 25)
+	messages, searched, err := client.Since(m.LastUID, 25)
 	if err != nil {
 		return 0, err
 	}
@@ -197,6 +197,14 @@ func (s *Server) SyncMailbox(ctx context.Context, user *store.User, m *store.Mai
 		s.hub.Publish(projectID, "task.created", toTaskJSON(*task))
 	}
 
+	// A run that got all the way through moves the marker to the whole of what the
+	// search considered, not merely to the last message it happened to read. That
+	// is what stops the same mail becoming a task again on the next run when the
+	// server did not put a uid in the fetch reply.
+	if ctx.Err() == nil && searched > highest {
+		highest = searched
+	}
+
 	// Written even when the loop was cut short, and outside the request's context
 	// so a cancelled request still records what it did.
 	if highest > m.LastUID {
diff --git a/internal/imap/imap.go b/internal/imap/imap.go
index ba4b6e8..fa27d22 100644
--- a/internal/imap/imap.go
+++ b/internal/imap/imap.go
@@ -16,15 +16,18 @@
 package imap
 
 import (
+	"bytes"
 	"crypto/tls"
 	"crypto/x509"
 	"fmt"
+	"io"
 	"net"
 	"strings"
 	"time"
 
 	"github.com/emersion/go-imap/v2"
 	"github.com/emersion/go-imap/v2/imapclient"
+	"github.com/emersion/go-message"
 )
 
 // Message is one mail, reduced to what a task needs.
@@ -108,9 +111,13 @@ func (c *Client) Close() error {
 // that consumed it would be taking something away. Flagging a mail is a deliberate
 // act with no other meaning, which is exactly what is wanted — the same reason the
 // Gmail side reads stars.
-func (c *Client) Since(uid uint32, limit int) ([]Message, error) {
+// The second return is the highest uid the search considered. A caller that got
+// through every message can move its marker to that, and then it does not matter
+// whether the server put a uid in each fetch reply — which some do not, and which
+// is how the same mail became a task again on every run.
+func (c *Client) Since(uid uint32, limit int) ([]Message, uint32, error) {
 	if _, err := c.c.Select(c.folder, &imap.SelectOptions{ReadOnly: true}).Wait(); err != nil {
-		return nil, fmt.Errorf("open %s: %w", c.folder, err)
+		return nil, 0, fmt.Errorf("open %s: %w", c.folder, err)
 	}
 
 	// From uid+1 to the end. A mailbox with nothing new answers with no uids
@@ -124,12 +131,12 @@ func (c *Client) Since(uid uint32, limit int) ([]Message, error) {
 	}
 	found, err := c.c.UIDSearch(criteria, nil).Wait()
 	if err != nil {
-		return nil, fmt.Errorf("search %s: %w", c.folder, err)
+		return nil, 0, fmt.Errorf("search %s: %w", c.folder, err)
 	}
 
 	uids := found.AllUIDs()
 	if len(uids) == 0 {
-		return nil, nil
+		return nil, uid, nil
 	}
 	if limit > 0 && len(uids) > limit {
 		// The newest ones. A mailbox flagged over years would otherwise make the
@@ -139,29 +146,51 @@ func (c *Client) Since(uid uint32, limit int) ([]Message, error) {
 
 	want := imap.UIDSetNum(uids...)
 	fetch := &imap.FetchOptions{
-		Envelope:    true,
-		UID:         true,
-		BodySection: []*imap.FetchItemBodySection{{Specifier: imap.PartSpecifierText, Peek: true}},
+		Envelope: true,
+		UID:      true,
+		// The whole message, headers included, so the MIME structure can be walked.
+		// TEXT alone gives the body as bytes — boundaries and part headers and all —
+		// which is what put "--=_be71cb39… Content-Transfer-Encoding: 8bit" at the
+		// front of every task made from a multipart mail.
+		BodySection: []*imap.FetchItemBodySection{{Peek: true}},
 	}
+	var highest uint32
+	for _, u := range uids {
+		if uint32(u) > highest {
+			highest = uint32(u)
+		}
+	}
+
 	msgs, err := c.c.Fetch(want, fetch).Collect()
 	if err != nil {
-		return nil, fmt.Errorf("fetch from %s: %w", c.folder, err)
+		return nil, 0, fmt.Errorf("fetch from %s: %w", c.folder, err)
 	}
 
 	out := make([]Message, 0, len(msgs))
-	for _, m := range msgs {
+	for i, m := range msgs {
 		if m.Envelope == nil {
 			continue
 		}
+
+		// The uid comes from the search when the fetch reply does not carry one.
+		// A missing uid is not cosmetic: it is the marker the next run starts from,
+		// and a marker stuck at zero makes every message arrive again on every run.
+		// That is what happened against a real server while the tests stayed green,
+		// because the server they run against always answers with it.
+		msgUID := uint32(m.UID)
+		if msgUID == 0 && i < len(uids) {
+			msgUID = uint32(uids[i])
+		}
+
 		out = append(out, Message{
-			UID:     uint32(m.UID),
+			UID:     msgUID,
 			From:    address(m.Envelope.From),
 			Subject: strings.TrimSpace(m.Envelope.Subject),
 			Snippet: snippet(m),
 			Date:    m.Envelope.Date,
 		})
 	}
-	return out, nil
+	return out, highest, nil
 }
 
 // address renders the first sender as "Name <addr>", or just the address.
@@ -177,23 +206,92 @@ func address(list []imap.Address) string {
 	return a.Name + " <" + addr + ">"
 }
 
-// snippet is the first readable line or so of the body.
+// snippet is the first readable text in the mail.
 //
-// No MIME walk and no HTML stripping yet: this is what shows under a task's title,
-// and a wrong-but-short line is a smaller problem than a parser that has to be
-// right about every mail ever sent. The full mail stays where it is.
+// It walks the MIME structure rather than taking the body as bytes. text/plain is
+// preferred and HTML is the fallback with its tags stripped — crudely, because
+// this is the line under a task's title and not a rendering engine. The mail
+// itself stays where it is.
 const snippetLimit = 400
 
 func snippet(m *imapclient.FetchMessageBuffer) string {
 	for _, body := range m.BodySection {
-		text := strings.TrimSpace(string(body.Bytes))
-		if text == "" {
-			continue
+		if text := readable(body.Bytes); text != "" {
+			return cut(text)
 		}
-		if len(text) > snippetLimit {
-			text = text[:snippetLimit] + "…"
-		}
-		return text
 	}
 	return ""
 }
+
+func readable(raw []byte) string {
+	entity, err := message.Read(bytes.NewReader(raw))
+	if err != nil {
+		// Not something this parser recognises. The raw bytes read badly but read,
+		// and a mail is not worth losing over its own headers.
+		return strings.TrimSpace(string(raw))
+	}
+	return strings.TrimSpace(fromEntity(entity, 0))
+}
+
+// fromEntity descends into a multipart mail. The depth guard is for the mail that
+// nests parts inside parts inside parts — rare, and cheaper to bound than to trust.
+func fromEntity(entity *message.Entity, depth int) string {
+	if depth > 4 {
+		return ""
+	}
+
+	if parts := entity.MultipartReader(); parts != nil {
+		var html string
+		for {
+			part, err := parts.NextPart()
+			if err != nil {
+				break
+			}
+			if text := fromEntity(part, depth+1); text != "" {
+				kind, _, _ := part.Header.ContentType()
+				if kind != "text/html" {
+					return text
+				}
+				if html == "" {
+					html = text
+				}
+			}
+		}
+		return html
+	}
+
+	body, _ := io.ReadAll(entity.Body)
+	kind, _, _ := entity.Header.ContentType()
+	if kind == "text/html" {
+		return stripTags(string(body))
+	}
+	return strings.TrimSpace(string(body))
+}
+
+// stripTags removes markup without pretending to understand it. Enough for one
+// line of preview, and honest about being no more than that.
+func stripTags(html string) string {
+	var b strings.Builder
+	depth := 0
+	for _, r := range html {
+		switch {
+		case r == '<':
+			depth++
+		case r == '>':
+			if depth > 0 {
+				depth--
+			}
+		case depth == 0:
+			b.WriteRune(r)
+		}
+	}
+	return strings.Join(strings.Fields(b.String()), " ")
+}
+
+func cut(text string) string {
+	runes := []rune(text)
+	if len(runes) > snippetLimit {
+		return string(runes[:snippetLimit]) + "…"
+	}
+	return text
+}
diff --git a/internal/imap/roundtrip_test.go b/internal/imap/roundtrip_test.go
index 5eea409..d96046a 100644
--- a/internal/imap/roundtrip_test.go
+++ b/internal/imap/roundtrip_test.go
@@ -37,7 +37,7 @@ func TestFlaggedMailComesBackAsMessages(t *testing.T) {
 	}
 	defer client.Close()
 
-	msgs, err := client.Since(0, 25)
+	msgs, _, err := client.Since(0, 25)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -59,7 +59,7 @@ func TestFlaggedMailComesBackAsMessages(t *testing.T) {
 
 	// And reading on from a marker returns only what is newer, which is the whole
 	// of the deduplication.
-	rest, err := client.Since(msgs[0].UID, 25)
+	rest, _, err := client.Since(msgs[0].UID, 25)
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -92,6 +92,9 @@ func TestAnUntrustedCertificateIsRefused(t *testing.T) {
 type mail struct {
 	subject, from, body string
 	flagged             bool
+	// raw replaces the whole message when set, which is the only way to get a
+	// genuinely multipart one in.
+	raw string
 }
 
 // serveMailbox starts an in-process IMAP server over TLS and returns its address
@@ -112,8 +115,11 @@ func serveMailbox(t *testing.T, mails []mail) (string, *x509.CertPool) {
 		if m.flagged {
 			flags = append(flags, imap.FlagFlagged)
 		}
-		raw := "From: " + m.from + "\r\nSubject: " + m.subject +
-			"\r\nDate: Tue, 18 Aug 2026 10:00:00 +0200\r\n\r\n" + m.body + "\r\n"
+		raw := m.raw
+		if raw == "" {
+			raw = "From: " + m.from + "\r\nSubject: " + m.subject +
+				"\r\nDate: Tue, 18 Aug 2026 10:00:00 +0200\r\n\r\n" + m.body + "\r\n"
+		}
 		if _, err := user.Append("INBOX", strings.NewReader(raw), &imap.AppendOptions{
 			Flags: flags,
 		}); err != nil {
@@ -181,3 +187,78 @@ func selfSigned(t *testing.T) (tls.Certificate, *x509.CertPool) {
 	pool.AppendCertsFromPEM(certPEM)
 	return cert, pool
 }
+
+// The bug this was written for: every press of "Fetch now" made the same mail
+// into a task again. The marker the next run starts from is the uid, and if it
+// comes back as zero the marker never moves.
+func TestEveryMessageCarriesAUID(t *testing.T) {
+	addr, pool := serveMailbox(t, []mail{
+		{subject: "En", from: "a@example.dk", body: "en", flagged: true},
+		{subject: "To", from: "b@example.dk", body: "to", flagged: true},
+	})
+	client, err := Dial(Account{Host: addr, Username: "kw", Password: "hemmelig", RootCAs: pool})
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer client.Close()
+
+	msgs, _, err := client.Since(0, 25)
+	if err != nil {
+		t.Fatal(err)
+	}
+	for _, m := range msgs {
+		if m.UID == 0 {
+			t.Fatalf("%q came back without a uid; the marker would never move and "+
+				"every run would make it into a task again", m.Subject)
+		}
+	}
+	if msgs[0].UID == msgs[1].UID {
+		t.Error("two messages share a uid")
+	}
+}
+
+// The other half of the same report: the snippet under a task's title read
+// "--=_be71cb39… Content-Transfer-Encoding: 8bit Content-Type: text/plain".
+func TestAMultipartMailReadsAsItsText(t *testing.T) {
+	const boundary = "=_be71cb3975bdfbc60a16327cb2f49c23"
+	body := "This is a multi-part message.\r\n" +
+		"--" + boundary + "\r\n" +
+		"Content-Transfer-Encoding: 8bit\r\n" +
+		"Content-Type: text/plain; charset=UTF-8; format=flowed\r\n\r\n" +
+		"Hej igen,\r\n\r\nVi har normalt 3 slags. :)\r\n" +
+		"--" + boundary + "\r\n" +
+		"Content-Type: text/html; charset=UTF-8\r\n\r\n" +
+		"<html><body><p>Hej igen</p></body></html>\r\n" +
+		"--" + boundary + "--\r\n"
+
+	addr, pool := serveMailbox(t, []mail{{
+		flagged: true,
+		raw: "Content-Type: multipart/alternative; boundary=\"" + boundary + "\"\r\n" +
+			"From: kontakt@mikrobagt.dk\r\nSubject: Re: Kaffebestilling\r\n" +
+			"Date: Tue, 18 Aug 2026 10:00:00 +0200\r\n\r\n" + body,
+	}})
+
+	client, err := Dial(Account{Host: addr, Username: "kw", Password: "hemmelig", RootCAs: pool})
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer client.Close()
+
+	msgs, _, err := client.Since(0, 25)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if len(msgs) != 1 {
+		t.Fatalf("got %d messages", len(msgs))
+	}
+
+	got := msgs[0].Snippet
+	for _, junk := range []string{boundary, "Content-Transfer-Encoding", "Content-Type", "<html>", "<p>"} {
+		if strings.Contains(got, junk) {
+			t.Errorf("the snippet still carries %q: %q", junk, got)
+		}
+	}
+	if !strings.HasPrefix(got, "Hej igen") {
+		t.Errorf("the snippet does not start with the text of the mail: %q", got)
+	}
+}