diff --git a/src/api/s3_copy.rs b/src/api/s3_copy.rs
index f8a269c0..1b2573a1 100644
--- a/src/api/s3_copy.rs
+++ b/src/api/s3_copy.rs
@@ -1,7 +1,8 @@
+use std::pin::Pin;
 use std::sync::Arc;
 use std::time::{Duration, SystemTime, UNIX_EPOCH};
 
-use futures::{stream, StreamExt, TryFutureExt};
+use futures::{stream, stream::Stream, StreamExt, TryFutureExt};
 use md5::{Digest as Md5Digest, Md5};
 
 use hyper::{Body, Request, Response};
@@ -316,118 +317,67 @@ pub async fn handle_upload_part_copy(
 			})
 		})
 		.peekable();
-	let mut source_blocks = Box::pin(source_blocks);
 
-	// Keep information about the next block we want to insert
+	// The defragmenter is a custom stream (defined below) that concatenates
+	// consecutive block parts when they are too small.
+	// It returns a series of (Vec<u8>, Option<Hash>).
+	// When it is done, it returns an empty vec.
+	// Same as the previous iterator, the Option is Some(_) if and only if
+	// it's an existing block of the Garage data store.
+	let mut defragmenter = Defragmenter::new(garage.config.block_size, Box::pin(source_blocks));
+
 	let mut current_offset = 0;
-	let mut next_block: Option<(Vec<u8>, Option<Hash>)> = None;
+	let mut next_block = defragmenter.next().await?;
 
-	// State of the defragmenter
-	let config_block_size = garage.config.block_size;
-	let mut defrag_buffer = vec![];
-	let mut defrag_hash = None;
-
-	// We loop a step that does two things concurrently:
-	// 1. if there is a block to be inserted in next_block, insert it
-	// 2. grab the next block (it might be composed of several sub-blocks
-	//    to be concatenated to ensure defragmentation)
 	loop {
-		let insert_current_block = async {
-			if let Some((data, existing_block_hash)) = next_block {
-				md5hasher.update(&data[..]);
-
-				let must_upload = existing_block_hash.is_none();
-				let final_hash = existing_block_hash.unwrap_or_else(|| blake2sum(&data[..]));
-
-				let mut version =
-					Version::new(dest_version_uuid, dest_bucket_id, dest_key.clone(), false);
-				version.blocks.put(
-					VersionBlockKey {
-						part_number,
-						offset: current_offset,
-					},
-					VersionBlock {
-						hash: final_hash,
-						size: data.len() as u64,
-					},
-				);
-				current_offset += data.len() as u64;
-
-				let block_ref = BlockRef {
-					block: final_hash,
-					version: dest_version_uuid,
-					deleted: false.into(),
-				};
-
-				let garage2 = garage.clone();
-				futures::try_join!(
-					// Thing 1: if the block is not exactly a block that existed before,
-					// we need to insert that data as a new block.
-					async move {
-						if must_upload {
-							garage2.block_manager.rpc_put_block(final_hash, data).await
-						} else {
-							Ok(())
-						}
-					},
-					// Thing 2: we need to insert the block in the version
-					garage.version_table.insert(&version),
-					// Thing 3: we need to add a block reference
-					garage.block_ref_table.insert(&block_ref),
-				)?;
-				Ok(())
-			} else {
-				Ok(())
-			}
-		};
-
-		let get_next_block = async {
-			loop {
-				let tmpres: Option<&Result<(Vec<u8>, Option<Hash>), garage_util::error::Error>> =
-					source_blocks.as_mut().peek().await;
-				if let Some(res) = tmpres {
-					let (next_block, _) = match res {
-						Ok(t) => t,
-						Err(_) => {
-							source_blocks.next().await.unwrap()?;
-							unreachable!()
-						}
-					};
-
-					if defrag_buffer.is_empty() {
-						let (next_block, next_block_hash) = source_blocks.next().await.unwrap()?;
-						defrag_buffer = next_block;
-						defrag_hash = next_block_hash;
-					} else if defrag_buffer.len() + next_block.len() > config_block_size {
-						return Ok((
-							std::mem::replace(&mut defrag_buffer, vec![]),
-							std::mem::replace(&mut defrag_hash, None),
-						));
-					} else {
-						let (next_block, _) = source_blocks.next().await.unwrap()?;
-						defrag_buffer.extend(next_block);
-						defrag_hash = None;
-					}
-				} else {
-					return Ok::<_, garage_util::error::Error>((
-						std::mem::replace(&mut defrag_buffer, vec![]),
-						std::mem::replace(&mut defrag_hash, None),
-					));
-				}
-			}
-		};
-
-		let tmp: Result<(_, (Vec<u8>, Option<Hash>)), garage_util::error::Error> = futures::try_join!(
-			insert_current_block,
-			// Thing 4: we need to prefetch the next block
-			get_next_block,
-		);
-		let tmp_block = tmp?.1;
-
-		if tmp_block.0.is_empty() {
+		let (data, existing_block_hash) = next_block;
+		if data.is_empty() {
 			break;
 		}
-		next_block = Some(tmp_block);
+
+		md5hasher.update(&data[..]);
+
+		let must_upload = existing_block_hash.is_none();
+		let final_hash = existing_block_hash.unwrap_or_else(|| blake2sum(&data[..]));
+
+		let mut version = Version::new(dest_version_uuid, dest_bucket_id, dest_key.clone(), false);
+		version.blocks.put(
+			VersionBlockKey {
+				part_number,
+				offset: current_offset,
+			},
+			VersionBlock {
+				hash: final_hash,
+				size: data.len() as u64,
+			},
+		);
+		current_offset += data.len() as u64;
+
+		let block_ref = BlockRef {
+			block: final_hash,
+			version: dest_version_uuid,
+			deleted: false.into(),
+		};
+
+		let garage2 = garage.clone();
+		let res = futures::try_join!(
+			// Thing 1: if the block is not exactly a block that existed before,
+			// we need to insert that data as a new block.
+			async move {
+				if must_upload {
+					garage2.block_manager.rpc_put_block(final_hash, data).await
+				} else {
+					Ok(())
+				}
+			},
+			// Thing 2: we need to insert the block in the version
+			garage.version_table.insert(&version),
+			// Thing 3: we need to add a block reference
+			garage.block_ref_table.insert(&block_ref),
+			// Thing 4: we need to prefetch the next block
+			defragmenter.next(),
+		)?;
+		next_block = res.3;
 	}
 
 	let data_md5sum = md5hasher.finalize();
@@ -600,6 +550,54 @@ impl CopyPreconditionHeaders {
 	}
 }
 
+type BlockStreamItemOk = (Vec<u8>, Option<Hash>);
+type BlockStreamItem = Result<BlockStreamItemOk, garage_util::error::Error>;
+
+struct Defragmenter<S: Stream<Item = BlockStreamItem>> {
+	block_size: usize,
+	block_stream: Pin<Box<stream::Peekable<S>>>,
+	buffer: Vec<u8>,
+	hash: Option<Hash>,
+}
+
+impl<S: Stream<Item = BlockStreamItem>> Defragmenter<S> {
+	fn new(block_size: usize, block_stream: Pin<Box<stream::Peekable<S>>>) -> Self {
+		Self {
+			block_size,
+			block_stream,
+			buffer: vec![],
+			hash: None,
+		}
+	}
+
+	async fn next(&mut self) -> BlockStreamItem {
+		// Fill buffer while we can
+		while let Some(res) = self.block_stream.as_mut().peek().await {
+			let (peeked_next_block, _) = match res {
+				Ok(t) => t,
+				Err(_) => {
+					self.block_stream.next().await.unwrap()?;
+					unreachable!()
+				}
+			};
+
+			if self.buffer.is_empty() {
+				let (next_block, next_block_hash) = self.block_stream.next().await.unwrap()?;
+				self.buffer = next_block;
+				self.hash = next_block_hash;
+			} else if self.buffer.len() + peeked_next_block.len() > self.block_size {
+				break;
+			} else {
+				let (next_block, _) = self.block_stream.next().await.unwrap()?;
+				self.buffer.extend(next_block);
+				self.hash = None;
+			}
+		}
+
+		return Ok((std::mem::take(&mut self.buffer), self.hash.take()));
+	}
+}
+
 #[derive(Debug, Serialize, PartialEq)]
 pub struct CopyObjectResult {
 	#[serde(rename = "LastModified")]