diff --git a/src/home/homework-luks.c b/src/home/homework-luks.c
index f51b6f6fbf..7132c7e389 100644
--- a/src/home/homework-luks.c
+++ b/src/home/homework-luks.c
@@ -1430,7 +1430,7 @@ int home_setup_luks(
                 if (run_mark_dirty(setup->image_fd, true) > 0)
                         setup->do_mark_clean = true;
 
-                if (!user_record_luks_discard(h)) {
+                if (!FLAGS_SET(flags, HOME_SETUP_LUKS_DONT_FALLOCATE) && !user_record_luks_discard(h)) {
                         r = run_fallocate(setup->image_fd, &st);
                         if (r < 0)
                                 return r;
@@ -1505,7 +1505,9 @@ int home_setup_luks(
                 if (user_record_luks_discard(h))
                         (void) run_fitrim(setup->root_fd);
 
-                setup->do_offline_fallocate = !(setup->do_offline_fitrim = user_record_luks_offline_discard(h));
+                setup->do_offline_fitrim = user_record_luks_offline_discard(h);
+                setup->do_offline_fallocate = !setup->do_offline_fitrim;
+                setup->tolerate_offline_fallocate_enospc = FLAGS_SET(flags, HOME_SETUP_LUKS_DONT_FALLOCATE);
         }
 
         if (!sd_id128_is_null(found_partition_uuid))
@@ -1609,7 +1611,7 @@ int home_activate_luks(
 
         r = home_setup_luks(
                         h,
-                        0,
+                        flags,
                         NULL,
                         setup,
                         cache,
diff --git a/src/home/homework.c b/src/home/homework.c
index 2aebe46f95..08762a8022 100644
--- a/src/home/homework.c
+++ b/src/home/homework.c
@@ -436,7 +436,10 @@ int home_setup_done(HomeSetup *setup) {
         if (setup->image_fd >= 0) {
                 if (setup->do_offline_fallocate) {
                         q = run_fallocate(setup->image_fd, NULL);
-                        if (q < 0)
+                        if (setup->tolerate_offline_fallocate_enospc &&
+                            ERRNO_IS_NEG_DISK_SPACE(q))
+                                log_warning_errno(q, "Failed to allocate backing file, ignoring: %m");
+                        else if (q < 0)
                                 r = q;
                 }
 
@@ -468,6 +471,7 @@ int home_setup_done(HomeSetup *setup) {
         setup->undo_dm = false;
         setup->do_offline_fitrim = false;
         setup->do_offline_fallocate = false;
+        setup->tolerate_offline_fallocate_enospc = false;
         setup->do_mark_clean = false;
 
         setup->dm_name = mfree(setup->dm_name);
@@ -1686,7 +1690,7 @@ static int home_update(UserRecord *h, Hashmap *blobs, UserRecord **ret) {
                 return user_record_clone(h, USER_RECORD_LOAD_MASK_SECRET|USER_RECORD_PERMISSIVE, ret);
         }
 
-        r = home_setup(h, flags, &setup, &cache, &header_home);
+        r = home_setup(h, flags | HOME_SETUP_LUKS_DONT_FALLOCATE, &setup, &cache, &header_home);
         if (r < 0)
                 return r;
 
@@ -1788,7 +1792,7 @@ static int home_passwd(UserRecord *h, UserRecord **ret_home) {
         if (r < 0)
                 return r;
 
-        r = home_setup(h, flags, &setup, &cache, &header_home);
+        r = home_setup(h, flags | HOME_SETUP_LUKS_DONT_FALLOCATE, &setup, &cache, &header_home);
         if (r < 0)
                 return r;
 
@@ -1866,7 +1870,7 @@ static int home_inspect(UserRecord *h, UserRecord **ret_home) {
         if (r < 0)
                 return r;
 
-        r = home_setup(h, flags, &setup, &cache, &header_home);
+        r = home_setup(h, flags | HOME_SETUP_LUKS_DONT_FALLOCATE, &setup, &cache, &header_home);
         if (r < 0)
                 return r;
 
diff --git a/src/home/homework.h b/src/home/homework.h
index 493ddbf294..75eea1835d 100644
--- a/src/home/homework.h
+++ b/src/home/homework.h
@@ -48,6 +48,7 @@ typedef struct HomeSetup {
         bool undo_mount:1;            /* Whether to unmount /run/systemd/user-home-mount */
         bool do_offline_fitrim:1;
         bool do_offline_fallocate:1;
+        bool tolerate_offline_fallocate_enospc:1;
         bool do_mark_clean:1;
         bool do_drop_caches:1;
 
@@ -82,6 +83,9 @@ typedef enum HomeSetupFlags {
         HOME_SETUP_RESIZE_DONT_GROW            = 1 << 4, /* If the resize would grow, gracefully terminate operation */
         HOME_SETUP_RESIZE_DONT_SHRINK          = 1 << 5, /* If the resize would shrink, gracefully terminate operation */
         HOME_SETUP_RESIZE_DONT_UNDO            = 1 << 6, /* Leave loopback/DM device context open after successful operation */
+
+        /* LUKS backend: */
+        HOME_SETUP_LUKS_DONT_FALLOCATE         = 1 << 7, /* Skip setup-time backing file allocation */
 } HomeSetupFlags;
 
 int home_setup_done(HomeSetup *setup);
diff --git a/test/units/TEST-46-HOMED.sh b/test/units/TEST-46-HOMED.sh
index ee0b249db0..a7cc3139d1 100755
--- a/test/units/TEST-46-HOMED.sh
+++ b/test/units/TEST-46-HOMED.sh
@@ -40,6 +40,22 @@ wait_for_state() {
     timeout 2m bash -c "until homectl inspect '${1:?}' | grep -F 'State: $2' >/dev/null; do sleep 2; done"
 }
 
+cleanup_update_auto_resize_mode_without_space() (
+    set +e
+
+    rm -f /tmp/no-space-update.create /home/no-space-update.filler /home/no-space-update.home
+
+    if homectl inspect no-space-update >/dev/null 2>&1; then
+        homectl deactivate no-space-update 2>/dev/null
+        wait_for_state no-space-update inactive 2>/dev/null
+        homectl remove no-space-update 2>/dev/null
+    fi
+
+    mount /home -o remount,size=290M || :
+    systemctl restart systemd-homed.service || :
+    return 0
+)
+
 FSTYPE="$(stat --file-system --format "%T" /)"
 
 systemctl start systemd-homed.service systemd-userdbd.socket
@@ -337,6 +353,105 @@ testcase_recovery_key_file() (
     rm -rf "$KEY_DIR"
 )
 
+testcase_update_auto_resize_mode_without_space() {
+    local blocks bsize create_output fill_mbytes fill_size filler home_size image
+    local fs_stat image_stat image_blocks image_size image_unallocated
+
+    create_output="/tmp/no-space-update.create"
+    filler="/home/no-space-update.filler"
+    home_size=512M
+    image="/home/no-space-update.home"
+
+    trap cleanup_update_auto_resize_mode_without_space RETURN ERR EXIT
+
+    mount /home -o remount,size="$home_size"
+
+    if ! NEWPASSWORD=xEhErW0ndafV4s \
+        homectl create no-space-update \
+        --storage=luks \
+        --disk-size=300M \
+        --auto-resize-mode=shrink-and-grow \
+        --luks-discard=no \
+        --luks-offline-discard=yes \
+        --image-path="$image" \
+        --luks-pbkdf-type=pbkdf2 \
+        --luks-pbkdf-time-cost=1ms \
+        --rate-limit-interval=1s \
+        --rate-limit-burst=1000 \
+        >"$create_output" 2>&1; then
+
+        if grep -F "System does not support selected storage backend" "$create_output" >/dev/null; then
+            cat "$create_output"
+            echo "LUKS storage backend not supported, skipping update without space test."
+            return 0
+        fi
+
+        cat "$create_output" >&2
+        return 1
+    fi
+    cat "$create_output"
+
+    PASSWORD=xEhErW0ndafV4s homectl update no-space-update --disk-size=max
+    wait_for_state no-space-update inactive
+
+    # Activation still fully allocates luksDiscard=no images while space is available.
+    PASSWORD=xEhErW0ndafV4s homectl activate no-space-update
+    wait_for_state no-space-update active
+    homectl deactivate no-space-update
+    wait_for_state no-space-update inactive
+
+    PASSWORD=xEhErW0ndafV4s homectl resize no-space-update 256M
+    wait_for_state no-space-update inactive
+
+    PASSWORD=xEhErW0ndafV4s homectl update no-space-update --disk-size=max
+    wait_for_state no-space-update inactive
+
+    image_stat="$(stat -c '%s %b' "$image")"
+    read -r image_size image_blocks <<<"$image_stat"
+    [[ "$image_size" =~ ^[0-9]+$ && "$image_blocks" =~ ^[0-9]+$ ]]
+    image_unallocated=$((image_size - image_blocks * 512))
+    fs_stat="$(stat --file-system --format "%a %S" /home)"
+    read -r blocks bsize <<<"$fs_stat"
+    [[ "$blocks" =~ ^[0-9]+$ && "$bsize" =~ ^[0-9]+$ ]]
+    fill_size=$((blocks * bsize - 128 * 1024 * 1024))
+    fill_mbytes=$((fill_size / 1024 / 1024))
+    if [[ "$fill_mbytes" -le 0 ]]; then
+        echo "Not enough free space to set up update without space test, skipping."
+        return 0
+    fi
+
+    # Leave enough room for the small identity update below, but not enough for the old full-image fallocate().
+    dd if=/dev/zero of="$filler" bs=1M count="$fill_mbytes"
+
+    fs_stat="$(stat --file-system --format "%a %S" /home)"
+    read -r blocks bsize <<<"$fs_stat"
+    [[ "$blocks" =~ ^[0-9]+$ && "$bsize" =~ ^[0-9]+$ ]]
+    if [[ "$image_unallocated" -le $((blocks * bsize)) ]]; then
+        printf 'Not enough backing space for the update test: '
+        printf 'image_unallocated=%s free_space=%s fill_mbytes=%s\n' \
+            "$image_unallocated" "$((blocks * bsize))" "$fill_mbytes"
+        return 0
+    fi
+
+    systemctl restart systemd-homed.service
+    wait_for_exist no-space-update
+
+    PASSWORD=xEhErW0ndafV4s homectl authenticate no-space-update
+
+    PASSWORD=xEhErW0ndafV4s homectl update no-space-update \
+        --luks-discard=yes \
+        --luks-offline-discard=no
+
+    PASSWORD=xEhErW0ndafV4s homectl update no-space-update \
+        --luks-discard=no \
+        --luks-offline-discard=yes
+
+    PASSWORD=xEhErW0ndafV4s NEWPASSWORD=yPN4N0fYNKUkOq homectl passwd no-space-update
+    PASSWORD=yPN4N0fYNKUkOq homectl update no-space-update --auto-resize-mode=off
+
+    homectl inspect no-space-update | grep -F "Auto Resize: off" >/dev/null
+}
+
 testcase_blob() {
     # blob directory tests
     # See docs/USER_RECORD_BLOB_DIRS.md