diff --git a/internal/database/database.go b/internal/database/database.go
index 248acee..a536e77 100644
--- a/internal/database/database.go
+++ b/internal/database/database.go
@@ -68,6 +68,18 @@ const (
 	sqliteHardHeapLimitBytes = 1610612736
 )
 
+// Settings of the ANALYZE that Analyze runs.
+const (
+	// analysisLimit is about how many rows of each index ANALYZE reads
+	// (PRAGMA analysis_limit); SQLite estimates the rest.
+	analysisLimit = 1000
+	// optimizeAllTables is the PRAGMA optimize mask that runs ANALYZE (0x2)
+	// on every table that has an index without statistics or whose size has
+	// changed tenfold since it was last analyzed, not only on the tables this
+	// connection has queried (0x10000).
+	optimizeAllTables = 0x10002
+)
+
 // Bounds on the work GetRandomPrefixesByLength does to pick its sample.
 const (
 	// maxPrefixesToShuffle is the most prefixes of one mask length that are
@@ -182,7 +194,6 @@ func (d *Database) Initialize() error {
 	// enough for the whole pool.
 	pragmas := []string{
 		"PRAGMA journal_mode=WAL", // Write-Ahead Logging
-		"PRAGMA analysis_limit=0", // Disable automatic ANALYZE
 		fmt.Sprintf("PRAGMA soft_heap_limit=%d", sqliteSoftHeapLimitBytes),
 		fmt.Sprintf("PRAGMA hard_heap_limit=%d", sqliteHardHeapLimitBytes),
 	}
@@ -2151,14 +2162,18 @@ func (d *Database) GetIPInfoContext(
 	return info, nil
 }
 
-// Vacuum runs incremental vacuum to reclaim unused pages without blocking
-// writes. It frees up to the specified number of pages per call (0 = all
-// freeable pages).
+// Vacuum runs incremental vacuum to return up to 1000 unused pages to the
+// filesystem. Like Analyze and Checkpoint, it holds the database lock, so it
+// and the batch writes wait for each other instead of failing on SQLite's
+// write lock.
 func (d *Database) Vacuum(ctx context.Context) error {
 	// Free up to 1000 pages per call (~4MB with default 4KB page size)
-	// This keeps each vacuum operation quick and non-blocking
+	// This keeps each vacuum operation quick
 	const pagesToFree = 1000
 
+	d.lock("Vacuum")
+	defer d.unlock()
+
 	rows, err := d.db.QueryContext(ctx,
 		fmt.Sprintf("PRAGMA incremental_vacuum(%d)", pagesToFree))
 	if err != nil {
@@ -2180,9 +2195,20 @@ func (d *Database) Vacuum(ctx context.Context) error {
 	return nil
 }
 
-// Analyze runs the SQLite ANALYZE command to update query planner statistics.
+// Analyze updates the query planner statistics. It runs ANALYZE, through
+// PRAGMA optimize, only on the tables that have an index without statistics or
+// whose size has changed tenfold since they were last analyzed: even with
+// analysisLimit, ANALYZE counts every entry of each index, so it takes longer
+// as the tables grow. It holds the database lock.
 func (d *Database) Analyze(ctx context.Context) error {
-	_, err := d.db.ExecContext(ctx, "ANALYZE")
+	d.lock("Analyze")
+	defer d.unlock()
+
+	// analysis_limit is a setting of the connection, so it is set in the same
+	// call as PRAGMA optimize, which runs both statements on one connection.
+	_, err := d.db.ExecContext(ctx, fmt.Sprintf(
+		"PRAGMA analysis_limit=%d; PRAGMA optimize=%#x",
+		analysisLimit, optimizeAllTables))
 	if err != nil {
 		return fmt.Errorf("failed to analyze database: %w", err)
 	}
@@ -2192,8 +2218,11 @@ func (d *Database) Analyze(ctx context.Context) error {
 
 // Checkpoint runs a WAL checkpoint to transfer data from the WAL to the main database.
 // Uses TRUNCATE mode which blocks writers briefly but ensures complete checkpoint,
-// keeping the WAL small for fast read performance.
+// keeping the WAL small for fast read performance. It holds the database lock.
 func (d *Database) Checkpoint(ctx context.Context) error {
+	d.lock("Checkpoint")
+	defer d.unlock()
+
 	_, err := d.db.ExecContext(ctx, "PRAGMA wal_checkpoint(TRUNCATE)")
 	if err != nil {
 		return fmt.Errorf("failed to checkpoint WAL: %w", err)
@@ -2214,21 +2243,26 @@ func (d *Database) Ping(ctx context.Context) error {
 	return nil
 }
 
+// The debug messages lock logs, with the operation's name, when it starts to
+// wait for the database mutex and when it holds it.
+const (
+	lockWaitMessage = "Acquiring database lock"
+	lockHeldMessage = "Database lock acquired"
+)
+
 // lock acquires the database mutex and logs debug information
 func (d *Database) lock(operation string) {
 	// Get caller information
 	_, file, line, _ := runtime.Caller(1)
 	caller := fmt.Sprintf("%s:%d", filepath.Base(file), line)
 
-	d.logger.Debug("Acquiring database lock",
-		"operation", operation, "caller", caller)
+	d.logger.Debug(lockWaitMessage, "operation", operation, "caller", caller)
 
 	d.mu.Lock()
 	d.lockedAt = time.Now()
 	d.lockedBy = fmt.Sprintf("%s (%s)", operation, caller)
 
-	d.logger.Debug("Database lock acquired",
-		"operation", operation, "caller", caller)
+	d.logger.Debug(lockHeldMessage, "operation", operation, "caller", caller)
 }
 
 // unlock releases the database mutex and logs debug information including
diff --git a/internal/database/database_internal_test.go b/internal/database/database_internal_test.go
index f2b2e63..d93b188 100644
--- a/internal/database/database_internal_test.go
+++ b/internal/database/database_internal_test.go
@@ -5,6 +5,7 @@ import (
 	"database/sql"
 	"errors"
 	"fmt"
+	"log/slog"
 	"net/netip"
 	"slices"
 	"sync"
@@ -47,6 +48,23 @@ const (
 	asnSecondBand = 100
 )
 
+// Parameters for the tests of maintenance and the database lock.
+const (
+	// lockMessageBuffer is how many lock messages a test database's logger
+	// holds before logging waits for the test to read them.
+	lockMessageBuffer = 64
+	// operationKey is the log attribute that names the operation taking the
+	// lock.
+	operationKey = "operation"
+	// testBatchWrite is the operation name the tests take the lock under.
+	testBatchWrite = "test batch write"
+	// lockWaitTimeout is the context timeout of a maintenance call that the
+	// tests let run out while it waits for the lock.
+	lockWaitTimeout = time.Millisecond
+	// lockTestASN is the AS the batch write in the lock tests stores.
+	lockTestASN = 64500
+)
+
 // Parameters for the prefix-length sample tests.
 const (
 	// sampleLimit is how many prefixes the tests ask the sample for.
@@ -474,14 +492,10 @@ func TestVacuumReturnsFreePages(t *testing.T) {
 	}
 }
 
-// TestBatchWriteDuringCheckpoint reproduces issue #25. A batch write reads
-// (SELECT) before it writes (INSERT/UPDATE). Under the default deferred locking
-// the transaction begins as a reader and, when the maintainer's WAL checkpoint
-// holds the write lock, its upgrade to writer fails immediately with "database
-// is locked" without honouring busy_timeout, dropping the batch. With
-// _txlock=immediate the transaction takes the write lock at BEGIN and waits, so
-// no batch is dropped. The checkpoint runs without the Database mutex, exactly
-// as the background maintainer does in production.
+// TestBatchWriteDuringCheckpoint runs checkpoints back to back while batch
+// writes run and checks that every batch write succeeds: a checkpoint holds the
+// database lock as a batch write does, and checkpoints must not keep batch
+// writes from getting it.
 func TestBatchWriteDuringCheckpoint(t *testing.T) {
 	t.Parallel()
 
@@ -530,6 +544,210 @@ func TestBatchWriteDuringCheckpoint(t *testing.T) {
 	wg.Wait()
 }
 
+// lockMessage is a debug message the database lock logged, and the name of the
+// operation that logged it.
+type lockMessage struct {
+	text      string
+	operation string
+}
+
+// lockMessages is a log handler that passes on each message the database lock
+// logs. The lock tests read it to know that an operation waits for the lock or
+// holds it, instead of guessing how long that takes.
+type lockMessages chan lockMessage
+
+// Enabled lets every message through, so the lock's debug messages arrive.
+func (m lockMessages) Enabled(context.Context, slog.Level) bool { return true }
+
+// Handle passes on a message that names an operation and drops the others.
+func (m lockMessages) Handle(_ context.Context, record slog.Record) error {
+	record.Attrs(func(attr slog.Attr) bool {
+		if attr.Key != operationKey {
+			return true
+		}
+
+		m <- lockMessage{text: record.Message, operation: attr.Value.String()}
+
+		return false
+	})
+
+	return nil
+}
+
+// WithAttrs returns m: the tests need no attributes added.
+func (m lockMessages) WithAttrs([]slog.Attr) slog.Handler { return m }
+
+// WithGroup returns m: the tests need no groups.
+func (m lockMessages) WithGroup(string) slog.Handler { return m }
+
+// newDatabaseWithLockMessages opens a new database whose logger passes the lock's
+// messages to the returned channel.
+func newDatabaseWithLockMessages(t *testing.T) (*Database, lockMessages) {
+	t.Helper()
+
+	messages := make(lockMessages, lockMessageBuffer)
+	cfg := &config.Config{StateDir: t.TempDir()}
+
+	db, err := New(cfg, &logger.Logger{Logger: slog.New(messages)})
+	if err != nil {
+		t.Fatalf("failed to create database: %v", err)
+	}
+
+	t.Cleanup(func() { _ = db.Close() })
+
+	return db, messages
+}
+
+// waitForLockMessage waits until operation logs text, and fails the test if
+// returned delivers first: the call running operation returned without logging
+// text.
+func waitForLockMessage(
+	t *testing.T,
+	messages lockMessages,
+	text, operation string,
+	returned <-chan error,
+) {
+	t.Helper()
+
+	for {
+		select {
+		case message := <-messages:
+			if message.text == text && message.operation == operation {
+				return
+			}
+		case err := <-returned:
+			t.Fatalf("%s returned (error: %v) without logging %q",
+				operation, err, text)
+		}
+	}
+}
+
+// TestVacuumWaitsForBatchWrite holds the database lock as a batch write does and
+// checks that Vacuum waits for it and then succeeds. Vacuum ran without the
+// lock, met the batch writes at SQLite's write lock and failed with "database
+// is locked" (https://git.eeqj.de/sneak/routewatch/issues/94).
+func TestVacuumWaitsForBatchWrite(t *testing.T) {
+	t.Parallel()
+
+	db, messages := newDatabaseWithLockMessages(t)
+
+	db.lock(testBatchWrite)
+
+	vacuumed := make(chan error, 1)
+
+	go func() { vacuumed <- db.Vacuum(context.Background()) }()
+
+	waitForLockMessage(t, messages, lockWaitMessage, "Vacuum", vacuumed)
+
+	db.unlock()
+
+	err := <-vacuumed
+	if err != nil {
+		t.Fatalf("Vacuum after the batch write: %v", err)
+	}
+}
+
+// TestBatchWriteWaitsForAnalyze keeps Analyze waiting for SQLite's write lock,
+// which another connection holds, and checks that a batch write started
+// meanwhile waits for Analyze to give up the database lock, that both then
+// succeed, and that Analyze stored statistics. ANALYZE ran without the database
+// lock, and a batch write that waited longer than the busy timeout for it failed
+// with "database is locked".
+func TestBatchWriteWaitsForAnalyze(t *testing.T) {
+	t.Parallel()
+
+	db, messages := newDatabaseWithLockMessages(t)
+	ctx := context.Background()
+	asns := map[int]time.Time{lockTestASN: time.Now().UTC()}
+
+	// A stored AS gives ANALYZE a table to analyze and statistics to write.
+	err := db.GetOrCreateASNBatch(asns)
+	if err != nil {
+		t.Fatalf("failed to store an AS: %v", err)
+	}
+
+	// With _txlock=immediate this transaction takes SQLite's write lock at
+	// BEGIN, so ANALYZE has to wait for it while Analyze holds the database lock.
+	writer, err := db.db.BeginTx(ctx, nil)
+	if err != nil {
+		t.Fatalf("failed to begin the transaction ANALYZE waits for: %v", err)
+	}
+
+	defer func() { _ = writer.Rollback() }()
+
+	analyzed := make(chan error, 1)
+
+	go func() { analyzed <- db.Analyze(ctx) }()
+
+	waitForLockMessage(t, messages, lockHeldMessage, "Analyze", analyzed)
+
+	written := make(chan error, 1)
+
+	go func() { written <- db.GetOrCreateASNBatch(asns) }()
+
+	waitForLockMessage(t, messages, lockWaitMessage, "GetOrCreateASNBatch", written)
+
+	err = writer.Rollback()
+	if err != nil {
+		t.Fatalf("failed to end the transaction ANALYZE waits for: %v", err)
+	}
+
+	err = <-analyzed
+	if err != nil {
+		t.Errorf("Analyze: %v", err)
+	}
+
+	err = <-written
+	if err != nil {
+		t.Errorf("batch write after Analyze: %v", err)
+	}
+
+	var statistics int
+
+	err = db.db.QueryRowContext(ctx,
+		"SELECT count(*) FROM sqlite_stat1 WHERE tbl = 'asns'").Scan(&statistics)
+	if err != nil {
+		t.Fatalf("failed to read the statistics: %v", err)
+	}
+
+	if statistics == 0 {
+		t.Error("Analyze stored no statistics for the asns table")
+	}
+}
+
+// TestCheckpointLockWaitEndsWithContext holds the database lock while the
+// context of a waiting Checkpoint times out, and checks that Checkpoint then
+// returns the context's error and leaves the lock free.
+func TestCheckpointLockWaitEndsWithContext(t *testing.T) {
+	t.Parallel()
+
+	db, messages := newDatabaseWithLockMessages(t)
+
+	db.lock(testBatchWrite)
+
+	ctx, cancel := context.WithTimeout(context.Background(), lockWaitTimeout)
+	defer cancel()
+
+	checkpointed := make(chan error, 1)
+
+	go func() { checkpointed <- db.Checkpoint(ctx) }()
+
+	waitForLockMessage(t, messages, lockWaitMessage, "Checkpoint", checkpointed)
+	<-ctx.Done()
+	db.unlock()
+
+	err := <-checkpointed
+	if !errors.Is(err, context.DeadlineExceeded) {
+		t.Fatalf("Checkpoint = %v, want %v", err, context.DeadlineExceeded)
+	}
+
+	if !db.mu.TryLock() {
+		t.Fatal("Checkpoint kept the database lock after its context ended")
+	}
+
+	db.mu.Unlock()
+}
+
 // TestGetRandomPrefixesByLengthListsPrefixOnce stores one prefix of each
 // family learned from two peers in the same second and checks that the
 // prefix-length sample lists each of them once.