diff --git a/melamine/classes.py b/melamine/classes.py
index 58fefca..6dc917a 100644
--- a/melamine/classes.py
+++ b/melamine/classes.py
@@ -155,7 +155,7 @@ class ShredFile(AsyncObject):
             if self.hardlinks:
                 log_buf = f"[5/4] Unlinking {len(self.hardlinks)} hardlinks"
                 if not dryrun:
-                    tasks = [link.unlink() for link in self.hardlinks]
+                    tasks = [link.unlink() for link in self.hardlinks if link.name != "." and link.name != ".."]
                     done, _ = await asyncio.wait(tasks)
                     for task in done:
                         e = task.exception()
diff --git a/melamine/shred.py b/melamine/shred.py
index a0bf80d..fd55310 100644
--- a/melamine/shred.py
+++ b/melamine/shred.py
@@ -27,32 +27,51 @@ async def main(job: argparse.Namespace) -> bool:
             raise TypeError(f"Not a file or directory: {path}")
     new_paths = set(await asyncio.gather(*tasks))
 
+    # Shred all physical files including hardlinks
+    for path in job.paths:
+        tasks = []
+        if isinstance(path, ShredFile):
+            tasks.append(path.shred(hash=job.exhaustive, dryrun=job.dryrun))
+        elif isinstance(path, ShredDir):
+            tasks.append(path.shred(hash=job.exhaustive, dryrun=job.dryrun))
+        done, _ = await asyncio.wait(*tasks)
+        for task in done:
+            e = task.exception()
+            if e:
+                logger.warning(f"Error raised while shredding: {e}")
+
     # Try to delete hardlinks based on the filesystem type
     job.paths = await get_all_hardlinks(new_paths)
 
     # Just in case, use "find" to delete any remaining hardlinks
-    # from the mount point
+    # from the mount point, so let's build a map of inodes to mount points
     logger.info("Deleting remaining hardlinks using find")
     inodes_in_mount_points = defaultdict(set)
     for path in job.paths:
         inodes_in_mount_points[path.mount_point].add(path.inode)
 
-    for mount_point, inodes in inodes_in_mount_points.items():
-        async for item in mount_point.rglob("*"):
-            if item.name == "." or item.name == "..":
-                continue
-            if item.stat().st_ino in inodes:
+    # We'll also limit concurrency to something reasonable since stat
+    # on an entire filesystem might be a bit burdensome
+    semaphore = asyncio.Semaphore(1024)
+
+    async def check_inode_and_unlink(item):
+        async with semaphore:
+            if await item.stat().st_ino in inodes_in_mount_points[item.mount_point]:
                 log_buf = f"Deleting hardlink: {item.path}"
                 if not job.dryrun:
                     log_buf = "DRY RUN " + log_buf
                     await item.path.unlink()
                 logger.info(log_buf)
 
-    # Shred all physical files including hardlinks
-    for path in job.paths:
-        if isinstance(path, ShredFile):
-            await path.shred(hash=job.exhaustive, dryrun=job.dryrun)
-        elif isinstance(path, ShredDir):
-            await path.shred(hash=job.exhaustive, dryrun=job.dryrun)
+    for mount_point, inodes in inodes_in_mount_points.items():
+        # checking for . and .. should not be neccessary w/ rglob
+        tasks = []
+        async for item in mount_point.rglob("*"):
+            tasks.append(check_inode_and_unlink(item))
+        done, _ = await asyncio.wait(*tasks)
+        for task in done:
+            e = task.exception()
+            if e:
+                logger.warning(f"Unable to unlink hardlink: {e}")
 
     logger.info("Done")