diff --git a/vamb/__main__.py b/vamb/__main__.py
index 51b9b53c..759dc438 100755
--- a/vamb/__main__.py
+++ b/vamb/__main__.py
@@ -1324,6 +1324,7 @@ def predict_taxonomy(
     cuda: bool,
 ) -> vamb.taxonomy.PredictedTaxonomy:
     begintime = time.time()
+    logger.info("Predicting taxonomy with Taxometer")
 
     taxonomies = vamb.taxonomy.Taxonomy.from_file(
         taxonomy_options.taxonomy.path, comp_metadata, False
@@ -1331,7 +1332,7 @@ def predict_taxonomy(
     nodes, ind_nodes, table_parent = vamb.taxvamb_encode.make_graph(
         taxonomies.contig_taxonomies
     )
-    logger.info(f"{len(nodes)} nodes in the graph")
+    logger.info(f"\t{len(nodes)} nodes in the graph")
     classes_order: list[str] = []
     for i in taxonomies.contig_taxonomies:
         if i is None or len(i.ranks) == 0:
@@ -1606,12 +1607,15 @@ def run_reclustering(opt: ReclusteringOptions):
             taxonomy = predicted_tax.to_taxonomy()
         else:
             tax_path = alg.taxonomy_options.path_or_tax_options.path
+            logger.info(f'Loading taxonomy from file "{tax_path}"')
             taxonomy = vamb.taxonomy.Taxonomy.from_file(
                 tax_path, composition.metadata, True
             )
         instantiated_alg = vamb.reclustering.DBScanAlgorithm(
             composition.metadata, taxonomy, opt.general.n_threads
         )
+        logger.info("Reclustering")
+        logger.info("\tAlgorithm: DBSCAN")
         reclustered_contigs = vamb.reclustering.recluster_bins(
             markers, latent, instantiated_alg
         )
@@ -1634,12 +1638,17 @@ def run_reclustering(opt: ReclusteringOptions):
                 s.add(vamb.reclustering.ContigId(i))
             clusters_as_ids.append(s)
         instantiated_alg = vamb.reclustering.KmeansAlgorithm(
-            clusters_as_ids, opt.general.seed, composition.metadata.identifiers
+            clusters_as_ids,
+            abs(opt.general.seed) % 4294967295,  # Note: sklearn seeds must be uint32
+            composition.metadata.lengths,
         )
+        logger.info("Reclustering")
+        logger.info("\tAlgorithm: KMeans")
         reclustered_contigs = vamb.reclustering.recluster_bins(
             markers, latent, instantiated_alg
         )
 
+    logger.info("\tReclustering complete")
     identifiers = composition.metadata.identifiers
     clusters_dict: dict[str, set[str]] = dict()
     for i, cluster in enumerate(reclustered_contigs):
diff --git a/vamb/reclustering.py b/vamb/reclustering.py
index 63f9c94d..45a3bdb4 100644
--- a/vamb/reclustering.py
+++ b/vamb/reclustering.py
@@ -23,15 +23,12 @@
 EPS_VALUES = np.arange(0.01, 0.35, 0.02)
 
 
-# TODO: This might be slightly algorithmically inefficient. The big problem is that it re-heapifies
-# the heap whenever a bin is emitted, which makes it O(N^2).
-# To solve this, I need some datastructure which is like a heap, but which allows me to update
-# arbitrary elements in the heap.
-# This can be solved with a MutableBinaryMaxHeap in Julia's DataStructures.jl, for inspiration.
+# This is a bottleneck, speed wise. Hence, we do a bunch of tricks to remove the
+# obviously bad bins to reduce computational cost.
 def deduplicate(
-    scoring: Callable[[set[ContigId]], float],
+    scoring: Callable[[Iterable[ContigId]], tuple[float, float]],
     bins: dict[BinId, set[ContigId]],
-) -> list[tuple[float, set[ContigId]]]:
+) -> list[set[ContigId]]:
     """
         deduplicate(f, bins)
 
@@ -41,14 +38,17 @@ def deduplicate(
     previously been returned from any other bin.
     Returns `list[tuple[float, set[ContigId]]]` with scored, disjoint bins.
     """
-    # We continuously mutate `bins`, so we need to make a copy here, so the caller
-    # doesn't have `bins` mutated inadvertently
-    bins = {b: s.copy() for (b, s) in bins.items()}
+    contig_sets = remove_duplicate_bins(bins.values())
+    scored_contig_sets = remove_badly_contaminated(scoring, contig_sets)
+    (to_deduplicate, result) = remove_unambigous_bins(scored_contig_sets)
+    bins = {BinId(i): b for (i, (b, _)) in enumerate(to_deduplicate)}
 
-    result: list[tuple[float, set[ContigId]]] = []
     # Use a heap, such that `heappop` will return the best bin
     # (Heaps in Python are min-heaps, so we use the negative score.)
-    heap: list[tuple[float, BinId]] = [(-scoring(c), b) for (b, c) in bins.items()]
+    heap = [
+        (-score_from_comp_cont(s), BinId(i))
+        for (i, (_, s)) in enumerate(to_deduplicate)
+    ]
     heapq.heapify(heap)
 
     # When removing the best bin, the contigs in that bin must be removed from all
@@ -62,9 +62,9 @@ def deduplicate(
             bins_of_contig[ci].add(b)
 
     while len(heap) > 0:
-        (neg_score, best_bin) = heapq.heappop(heap)
+        (_, best_bin) = heapq.heappop(heap)
         contigs = bins[best_bin]
-        result.append((-neg_score, contigs))
+        result.append(contigs)
 
         to_recompute.clear()
         for contig in contigs:
@@ -81,11 +81,13 @@ def deduplicate(
                         del bins[bin]
                     to_recompute.add(bin)
 
-            # Remove the bin we picked as the best
-            del bins[best_bin]
+        # Remove the bin we picked as the best
+        del bins[best_bin]
 
         # Check this here to skip recomputing scores and re-heapifying, since that
         # takes time.
+        # TODO: Could possibly skip this sometimes, if we know that any of the recomputed
+        # has a score lower than the next from the heap (and the heap top is not to be recomputed)
         if len(to_recompute) > 0:
             heap = [(s, b) for (s, b) in heap if b not in to_recompute]
             for bin in to_recompute:
@@ -94,18 +96,74 @@ def deduplicate(
                 # These empty bins should be discarded
                 c = bins.get(bin, None)
                 if c is not None:
-                    heap.append((-scoring(c), bin))
+                    heap.append((-score_from_comp_cont(scoring(c)), bin))
             heapq.heapify(heap)
 
     return result
 
 
+def remove_duplicate_bins(sets: Iterable[set[ContigId]]) -> list[set[ContigId]]:
+    seen_sets: set[frozenset[ContigId]] = set()
+    seen_singletons: set[ContigId] = set()
+    for contig_set in sets:
+        if len(contig_set) == 1:
+            seen_singletons.add(next(iter(contig_set)))
+        else:
+            fz = frozenset(contig_set)
+            if fz not in seen_sets:
+                seen_sets.add(fz)
+
+    result: list[set[ContigId]] = [{s} for s in seen_singletons]
+    for st in seen_sets:
+        result.append(set(st))
+    return result
+
+
+def remove_badly_contaminated(
+    scorer: Callable[[Iterable[ContigId]], tuple[float, float]],
+    sets: Iterable[set[ContigId]],
+) -> list[tuple[set[ContigId], tuple[float, float]]]:
+    result: list[tuple[set[ContigId], tuple[float, float]]] = []
+    max_contamination = 1.0
+    for contig_set in sets:
+        (completeness, contamination) = scorer(contig_set)
+        if contamination <= max_contamination:
+            result.append((contig_set, (completeness, contamination)))
+    return result
+
+
+def remove_unambigous_bins(
+    sets: list[tuple[set[ContigId], tuple[float, float]]],
+) -> tuple[list[tuple[set[ContigId], tuple[float, float]]], list[set[ContigId]]]:
+    """Remove all bins from d for which all the contigs are only present in that one bin,
+    and put them in the returned list.
+    These contigs have a trivial, unambiguous assignment.
+    """
+    in_single_bin: dict[ContigId, bool] = dict()
+    for contig_set, _ in sets:
+        for contig in contig_set:
+            existing = in_single_bin.get(contig)
+            if existing is None:
+                in_single_bin[contig] = True
+            elif existing is True:
+                in_single_bin[contig] = False
+    to_deduplicate: list[tuple[set[ContigId], tuple[float, float]]] = []
+    unambiguous: list[set[ContigId]] = []
+    for contig_set, scores in sets:
+        if all(in_single_bin[c] for c in contig_set):
+            unambiguous.append(contig_set)
+        else:
+            to_deduplicate.append((contig_set, scores))
+    return (to_deduplicate, unambiguous)
+
+
 class KmeansAlgorithm:
     "Arguments needed specifically when using the KMeans algorithm"
 
     def __init__(
         self, clusters: list[set[ContigId]], random_seed: int, contiglengths: np.ndarray
     ):
+        assert np.issubdtype(contiglengths.dtype, np.integer)
         self.contiglengths = contiglengths
         self.clusters = clusters
         self.random_seed = random_seed
@@ -138,6 +196,9 @@ def recluster_bins(
     latent: np.ndarray,
     algorithm: Union[KmeansAlgorithm, DBScanAlgorithm],
 ) -> list[set[ContigId]]:
+    assert np.issubdtype(algorithm.contiglengths.dtype, np.integer)
+    assert np.issubdtype(latent.dtype, np.floating)
+
     if not (len(algorithm.contiglengths) == markers.n_seqs == len(latent)):
         raise ValueError(
             "Number of elements in contiglengths, markers and latent must match"
@@ -171,6 +232,9 @@ def recluster_kmeans(
     random_seed: int,
 ) -> list[set[ContigId]]:
     assert len(latent) == len(contiglengths) == markers.n_seqs
+    assert np.issubdtype(contiglengths.dtype, np.integer)
+    assert np.issubdtype(latent.dtype, np.floating)
+    assert latent.ndim == 2
 
     result: list[set[ContigId]] = []
     indices_by_medoid: dict[int, set[ContigId]] = defaultdict(set)
@@ -203,7 +267,7 @@ def recluster_kmeans(
             median_counts,
         )
 
-        cluster_indices = np.ndarray(list(cluster))
+        cluster_indices = np.array(list(cluster))
         cluter_latent = latent[cluster_indices]
         cluster_lengths = contiglengths[cluster_indices]
         seed_latent = latent[seeds]
@@ -271,15 +335,18 @@ def get_kmeans_seeds(
     return result
 
 
-# An arbitrary score of a bin, where higher numbers is better.
-# completeness - 5 * contamination is used by the CheckM group as a heuristic.
-def score_bin(bin: set[ContigId], markers: Markers) -> float:
-    counts = count_markers(bin, markers)
+def get_completeness_contamination(counts: np.ndarray) -> tuple[float, float]:
     n_total = counts.sum()
     n_unique = (counts > 0).sum()
     completeness = n_unique / len(counts)
     contamination = (n_total - n_unique) / len(counts)
-    return completeness - 5 * contamination
+    return (completeness, contamination)
+
+
+# An arbitrary score of a bin, where higher numbers is better.
+# completeness - 5 * contamination is used by the CheckM group as a heuristic.
+def score_from_comp_cont(comp_cont: tuple[float, float]) -> float:
+    return comp_cont[0] - 5 * comp_cont[1]
 
 
 def recluster_dbscan(
@@ -342,8 +409,9 @@ def dbscan_genus(
     # present in one output bin, using the scoring function to greedily
     # output the best of the redundant bins.
     bin_dict = {BinId(i): c for (i, c) in enumerate(redundant_bins)}
-    scored_deduplicated = deduplicate(lambda x: score_bin(x, markers), bin_dict)
-    return [b for (_, b) in scored_deduplicated]
+    return deduplicate(
+        lambda x: get_completeness_contamination(count_markers(x, markers)), bin_dict
+    )
 
 
 def group_indices_by_genus(
@@ -358,4 +426,4 @@ def group_indices_by_genus(
         # Currently, we just skip it here
         if genus is not None:
             by_genus[genus].append(ContigId(i))
-    return {g: np.ndarray(i, dtype=np.int32) for (g, i) in by_genus.items()}
+    return {g: np.array(i, dtype=np.int32) for (g, i) in by_genus.items()}