diff --git a/src/lib.rs b/src/lib.rs
index c71d737..c1e6380 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -700,6 +700,44 @@ impl<F: Read + Seek> CompoundFile<F> {
             max_buffer_size,
         })
     }
+    /// Writes a compacted copy of this compound file to `dest`, and returns
+    /// the copy.  `dest` should be empty; it is written from the start.
+    ///
+    /// The copy has the same version and holds the same storages and streams,
+    /// with the same CLSIDs, state bits, and timestamps, but takes up only as
+    /// much space as those need.  A compound file never shrinks in place, so
+    /// the sectors freed by removing or shrinking streams stay in the file
+    /// until it is copied like this.  This is the approach Windows takes as
+    /// well: compacting a file means copying its root storage into a new one.
+    pub fn copy_to<W: Read + Write + Seek>(
+        &mut self,
+        dest: W,
+    ) -> io::Result<CompoundFile<W>> {
+        let mut copy =
+            CompoundFile::create_with_version(self.version(), dest)?;
+        let entries: Vec<Entry> = self.walk().collect();
+        for entry in entries.iter() {
+            if entry.is_stream() {
+                let mut source = self.open_stream(entry.path())?;
+                let mut target = copy.create_stream(entry.path())?;
+                io::copy(&mut source, &mut target)?;
+            } else if !entry.is_root() {
+                copy.create_storage(entry.path())?;
+            }
+        }
+        // Fill in the metadata once the tree is complete, so that nothing
+        // done while building it can overwrite what was copied.
+        for entry in entries.iter() {
+            copy.set_state_bits(entry.path(), entry.state_bits())?;
+            if !entry.is_stream() {
+                copy.set_storage_clsid(entry.path(), *entry.clsid())?;
+                copy.set_created_time(entry.path(), entry.created())?;
+                copy.set_modified_time(entry.path(), entry.modified())?;
+            }
+        }
+        copy.flush()?;
+        Ok(copy)
+    }
 }
 
 impl<F> CompoundFile<F> {
diff --git a/tests/copy_to.rs b/tests/copy_to.rs
new file mode 100644
index 0000000..e455f8f
--- /dev/null
+++ b/tests/copy_to.rs
@@ -0,0 +1,160 @@
+use cfb::{CompoundFile, Version};
+use std::io::{Cursor, Read, Seek, SeekFrom, Write};
+use std::path::PathBuf;
+use std::time::{Duration, SystemTime, UNIX_EPOCH};
+use uuid::Uuid;
+
+//===========================================================================//
+
+fn pattern(len: usize, seed: u8) -> Vec<u8> {
+    (0..len).map(|i| (i as u8).wrapping_mul(37).wrapping_add(seed)).collect()
+}
+
+fn epoch_plus(secs: u64) -> SystemTime {
+    UNIX_EPOCH + Duration::from_secs(secs)
+}
+
+/// Builds a file with nested storages, mini and regular streams, metadata on
+/// several entries, and wasted space from a removed and a shrunk stream.
+fn build_source(version: Version) -> CompoundFile<Cursor<Vec<u8>>> {
+    let mut comp =
+        CompoundFile::create_with_version(version, Cursor::new(Vec::new()))
+            .unwrap();
+    comp.create_storage("/a").unwrap();
+    comp.create_storage_all("/a/b/c").unwrap();
+    comp.create_stream("/small").unwrap().write_all(&pattern(100, 1)).unwrap();
+    comp.create_stream("/a/empty").unwrap();
+    comp.create_stream("/a/b/c/mid")
+        .unwrap()
+        .write_all(&pattern(5000, 2))
+        .unwrap();
+    {
+        let mut stream = comp.create_stream("/a/large").unwrap();
+        stream.write_all(&pattern(200_000, 4)).unwrap();
+        stream.set_len(100_000).unwrap();
+    }
+    // Written last, so that nothing reuses its sectors once it is gone.
+    comp.create_stream("/junk")
+        .unwrap()
+        .write_all(&pattern(300_000, 3))
+        .unwrap();
+    comp.remove_stream("/junk").unwrap();
+    comp.set_storage_clsid("/", Uuid::from_u128(0x1111)).unwrap();
+    comp.set_storage_clsid("/a/b", Uuid::from_u128(0x2222)).unwrap();
+    comp.set_state_bits("/small", 0x1234).unwrap();
+    comp.set_state_bits("/a", 0x5678).unwrap();
+    comp.set_created_time("/a", epoch_plus(1_000_000)).unwrap();
+    comp.set_modified_time("/a/b/c", epoch_plus(2_000_000)).unwrap();
+    comp.set_modified_time("/", epoch_plus(3_000_000)).unwrap();
+    comp
+}
+
+type Snapshot = Vec<(PathBuf, bool, u64, Uuid, u32, SystemTime, SystemTime)>;
+
+fn snapshot<F>(comp: &CompoundFile<F>) -> Snapshot {
+    comp.walk()
+        .map(|e| {
+            (
+                e.path().to_path_buf(),
+                e.is_stream(),
+                e.len(),
+                *e.clsid(),
+                e.state_bits(),
+                e.created(),
+                e.modified(),
+            )
+        })
+        .collect()
+}
+
+fn stream_contents<F: Read + Seek>(
+    comp: &mut CompoundFile<F>,
+) -> Vec<(PathBuf, Vec<u8>)> {
+    let paths: Vec<PathBuf> = comp
+        .walk()
+        .filter(|e| e.is_stream())
+        .map(|e| e.path().to_path_buf())
+        .collect();
+    paths
+        .into_iter()
+        .map(|path| {
+            let mut data = Vec::new();
+            comp.open_stream(&path).unwrap().read_to_end(&mut data).unwrap();
+            (path, data)
+        })
+        .collect()
+}
+
+//===========================================================================//
+
+#[test]
+fn copy_preserves_tree_metadata_and_contents() {
+    for version in [Version::V3, Version::V4] {
+        let mut source = build_source(version);
+        let mut copy = source.copy_to(Cursor::new(Vec::new())).unwrap();
+        assert_eq!(copy.version(), version);
+        assert_eq!(snapshot(&copy), snapshot(&source));
+        assert_eq!(stream_contents(&mut copy), stream_contents(&mut source));
+        assert_eq!(
+            copy.entry("/a/large").unwrap().len(),
+            100_000,
+            "shrunk stream keeps its new length"
+        );
+
+        // The copy must also hold up on disk, under strict validation.
+        let mut reopened =
+            CompoundFile::open_strict(copy.into_inner()).unwrap();
+        assert_eq!(snapshot(&reopened), snapshot(&source));
+        assert_eq!(
+            stream_contents(&mut reopened),
+            stream_contents(&mut source)
+        );
+    }
+}
+
+#[test]
+fn copy_drops_the_space_of_removed_and_shrunk_streams() {
+    let mut source = build_source(Version::V4);
+    let copy = source.copy_to(Cursor::new(Vec::new())).unwrap();
+    let source_len = source.into_inner().into_inner().len();
+    let copy_len = copy.into_inner().into_inner().len();
+    // The source still holds every sector the removed stream and the shrunk
+    // one ever used; the copy holds only the 105 KB that is live plus a few
+    // sectors of metadata.
+    assert!(source_len > 400_000, "source is {} bytes", source_len);
+    assert!(copy_len < 140_000, "copy is {} bytes", copy_len);
+}
+
+#[test]
+fn copy_from_a_read_only_source() {
+    let bytes = build_source(Version::V3).into_inner().into_inner();
+    // A `Cursor<&[u8]>` can be read and seeked but not written.
+    let mut source =
+        CompoundFile::open(Cursor::new(bytes.as_slice())).unwrap();
+    let mut copy = source.copy_to(Cursor::new(Vec::new())).unwrap();
+    assert_eq!(snapshot(&copy), snapshot(&source));
+    assert_eq!(stream_contents(&mut copy), stream_contents(&mut source));
+}
+
+#[test]
+fn copy_of_an_empty_file() {
+    let mut source = CompoundFile::create(Cursor::new(Vec::new())).unwrap();
+    let copy = source.copy_to(Cursor::new(Vec::new())).unwrap();
+    assert_eq!(snapshot(&copy), snapshot(&source));
+    CompoundFile::open_strict(copy.into_inner()).unwrap();
+}
+
+#[test]
+fn copy_leaves_the_source_readable() {
+    let mut source = build_source(Version::V3);
+    let before = snapshot(&source);
+    source.copy_to(Cursor::new(Vec::new())).unwrap();
+    assert_eq!(snapshot(&source), before);
+    let mut stream = source.open_stream("/a/b/c/mid").unwrap();
+    stream.seek(SeekFrom::Start(4000)).unwrap();
+    let mut tail = Vec::new();
+    stream.read_to_end(&mut tail).unwrap();
+    assert_eq!(tail, pattern(5000, 2)[4000..]);
+}
+
+//===========================================================================//