diff --git a/sourmash/VERSION b/sourmash/VERSION
index 758664dff..4b23e04d2 100644
--- a/sourmash/VERSION
+++ b/sourmash/VERSION
@@ -1 +1 @@
-2.0.0a6
+2.0.0a7
diff --git a/sourmash/sbt.py b/sourmash/sbt.py
index 5e6d1a4e5..fc2907533 100644
--- a/sourmash/sbt.py
+++ b/sourmash/sbt.py
@@ -305,7 +305,7 @@ def save(self, path, storage=None, sparseness=0.0):
         str
             full path to the new SBT description
         """
-        version = 3
+        version = 4
 
         if path.endswith('.sbt.json'):
             path = path[:-9]
@@ -395,6 +395,7 @@ def load(cls, location, leaf_loader=None, storage=None):
             1: cls._load_v1,
             2: cls._load_v2,
             3: cls._load_v3,
+            4: cls._load_v4,
         }
 
         # @CTB hack: check to make sure khmer Nodegraph supports the
@@ -524,27 +525,71 @@ def _load_v3(cls, info, leaf_loader, dirname, storage):
         # TODO: this might not be true with combine...
         tree.next_node = max_node
 
-        tree._fill_max_n_below()
+        tree._fill_min_n_below()
 
         return tree
 
-    def _fill_max_n_below(self):
+    @classmethod
+    def _load_v4(cls, info, leaf_loader, dirname, storage):
+        nodes = {int(k): v for (k, v) in info['nodes'].items()}
+
+        if not nodes:
+            raise ValueError("Empty tree!")
+
+        sbt_nodes = defaultdict(lambda: None)
+
+        klass = STORAGES[info['storage']['backend']]
+        if info['storage']['backend'] == "FSStorage":
+            storage = FSStorage(dirname, info['storage']['args']['path'])
+        elif storage is None:
+            storage = klass(**info['storage']['args'])
+
+        factory = GraphFactory(*info['factory']['args'])
+
+        max_node = 0
+        for k, node in nodes.items():
+            if node is None:
+                continue
+
+            if 'internal' in node['name']:
+                node['factory'] = factory
+                sbt_node = Node.load(node, storage)
+            else:
+                sbt_node = leaf_loader(node, storage)
+
+            sbt_nodes[k] = sbt_node
+            max_node = max(max_node, k)
+
+        tree = cls(factory, d=info['d'], storage=storage)
+        tree.nodes = sbt_nodes
+        tree.missing_nodes = {i for i in range(max_node)
+                                if i not in sbt_nodes}
+        # TODO: this might not be true with combine...
+        tree.next_node = max_node
+
+        return tree
+
+    def _fill_min_n_below(self):
+        """\
+        Propagate the smallest hash size below each node up the tree from
+        the leaves.
+        """
         for i, n in self.nodes.items():
             if isinstance(n, Leaf):
                 parent = self.parent(i)
                 if parent.pos not in self.missing_nodes:
-                    max_n_below = parent.node.metadata.get('max_n_below', 0)
-                    max_n_below = max(len(n.data.minhash.get_mins()),
-                                      max_n_below)
-                    parent.node.metadata['max_n_below'] = max_n_below
+                    min_n_below = parent.node.metadata.get('min_n_below', 1)
+                    min_n_below = min(len(n.data.minhash.get_mins()),
+                                      min_n_below)
+                    parent.node.metadata['min_n_below'] = min_n_below
 
                     current = parent
                     parent = self.parent(parent.pos)
                     while parent and parent.pos not in self.missing_nodes:
-                        max_n_below = parent.node.metadata.get('max_n_below', 0)
-                        max_n_below = max(current.node.metadata['max_n_below'],
-                                          max_n_below)
-                        parent.node.metadata['max_n_below'] = max_n_below
+                        min_n_below = parent.node.metadata.get('min_n_below', 1)
+                        min_n_below = min(current.node.metadata['min_n_below'],
+                                          min_n_below)
+                        parent.node.metadata['min_n_below'] = min_n_below
                         current = parent
                         parent = self.parent(parent.pos)
 
@@ -699,9 +744,9 @@ def load(info, storage=None):
 
     def update(self, parent):
         parent.data.update(self.data)
-        max_n_below = max(parent.metadata.get('max_n_below', 0),
-                          self.metadata.get('max_n_below'))
-        parent.metadata['max_n_below'] = max_n_below
+        min_n_below = min(parent.metadata.get('min_n_below', 1),
+                          self.metadata.get('min_n_below'))
+        parent.metadata['min_n_below'] = min_n_below
 
 
 class Leaf(object):
diff --git a/sourmash/sbtmh.py b/sourmash/sbtmh.py
index 631772937..1fc6e39f1 100644
--- a/sourmash/sbtmh.py
+++ b/sourmash/sbtmh.py
@@ -54,10 +54,11 @@ def save(self, path):
     def update(self, parent):
         for v in self.data.minhash.get_mins():
             parent.data.count(v)
-        max_n_below = parent.metadata.get('max_n_below', 0)
-        max_n_below = max(len(self.data.minhash.get_mins()),
-                          max_n_below)
-        parent.metadata['max_n_below'] = max_n_below
+        min_n_below = parent.metadata.get('min_n_below', 1)
+        min_n_below = min(len(self.data.minhash.get_mins()),
+                          min_n_below)
+
+        parent.metadata['min_n_below'] = min_n_below
 
     @property
     def data(self):
@@ -72,7 +73,39 @@ def data(self, new_data):
         self._data = new_data
 
 
+### Search functionality.
+
+def _max_jaccard_underneath_internal_node(node, hashes):
+    """\
+    calculate the maximum possibility similarity score below
+    this node, based on the number of matches in 'hashes' at this node,
+    divided by the smallest minhash size below this node.
+
+    This should yield be an upper bound on the Jaccard similarity
+    for any signature below this point.
+    """
+    if len(hashes) == 0:
+        return 0.0
+
+    # count the maximum number of hash matches beneath this node
+    matches = sum(1 for value in hashes if node.data.get(value))
+
+    # get the size of the smallest collection of hashes below this point
+    min_n_below = node.metadata.get('min_n_below', -1)
+
+    if min_n_below == -1:
+        raise Exception('cannot do similarity search on this SBT; need to rebuild.')
+
+    # max of numerator divided by min of denominator => max Jaccard
+    max_score = float(matches) / min_n_below
+
+    return max_score
+    
+
 def search_minhashes(node, sig, threshold, results=None, downsample=True):
+    """\
+    Default tree search function, searching for best Jaccard similarity.
+    """
     mins = sig.minhash.get_mins()
     score = 0
 
@@ -88,13 +121,8 @@ def search_minhashes(node, sig, threshold, results=None, downsample=True):
             else:
                 raise
 
-    else:  # Node or Leaf, Nodegraph by minhash comparison
-        if len(mins):
-            matches = sum(1 for value in mins if node.data.get(value))
-            max_mins = node.metadata.get('max_n_below', -1)
-            if max_mins == -1:
-                raise Exception('cannot do similarity search on this SBT; need to rebuild.')
-            score = float(matches) / max_mins
+    else:  # Node minhash comparison
+        score = _max_jaccard_underneath_internal_node(node, mins)
 
     if results is not None:
         results[node.name] = score
@@ -126,18 +154,13 @@ def search(self, node, sig, threshold, results=None):
                 else:
                     raise
         else:  # internal object, not leaf.
-            if len(mins):
-                matches = sum(1 for value in mins if node.data.get(value))
-                max_mins = node.metadata.get('max_n_below', -1)
-                if max_mins == -1:
-                    raise Exception('cannot do similarity search on this SBT; need to rebuild.')
-                score = float(matches) / max_mins
+            score = _max_jaccard_underneath_internal_node(node, mins)
 
         if results is not None:
             results[node.name] = score
 
         if score >= threshold:
-            # have we done better than this? if yes, truncate.
+            # have we done better than this elsewhere? if yes, truncate.
             if score > self.best_match:
                 # update best if it's a leaf node...
                 if isinstance(node, SigLeaf):
diff --git a/tests/test-data/sbt-search-bug/bacteroides.sig b/tests/test-data/sbt-search-bug/bacteroides.sig
new file mode 100644
index 000000000..7047f1dbf
--- /dev/null
+++ b/tests/test-data/sbt-search-bug/bacteroides.sig
@@ -0,0 +1 @@
+[{"class":"sourmash_signature","email":"","filename":"4.fa","hash_function":"0.murmur64","license":"CC0","name":"AE015928.1 Bacteroides thetaiotaomicron VPI-5482, complete genome","signatures":[{"ksize":21,"max_hash":18446744073709552,"md5sum":"d63ac939f501a4fe59cb4d65a42197a8","mins":[30516258945,248407864107,4506936415224,5725732573392,6323771032967,7376394466264,9171598155262,10000852515568,13849008543943,19569849799527,25235107494091,25880876164217,31953239569438,36118761561017,37051854750052,37618469915182,39013450701064,40274174228589,50308566489962,52034543982148,52343870018294,54554074482604,55385843090934,56197074550996,61351070762503,65970281182030,66035602071250,67088932092550,78521983227037,78833228090022,81243150582901,81413390972327,82205445482867,87238731653427,90619229004163,92292480389839,101265797905957,103567279961313,104144954753986,104981420828733,115503707518961,118849995302887,118948085322619,120890025010053,123921656087771,141096005167352,144513650872982,148523106903856,150575390872082,151994084484451,153001733970359,153876478855374,158949217646491,160569377373089,162157215310860,162741834961334,164188233911603,166898714872610,171865488063152,173118359783520,173437633770570,174035498867135,180813135421008,182155574520986,187760588234684,188095334979315,189925752912498,195031094671334,196538711246138,196927237367225,198327638542465,198753402223683,204482419059564,205573467384593,205921416017121,206755455778790,206947443698854,208754131887520,212608015065256,219790265490650,221445203577165,223178007614086,245941848684763,246563787439912,247306119559962,253488124914067,254873251507606,261912814401660,264947900319403,265007798019627,266472174419898,270022923236341,270278008295022,270950551557457,271711827099315,278762008121776,279298212944173,280244829038959,284481281356302,287192687224127,292964114607166,297268558864910,307818116813463,310465538045485,313596239135542,313716108310894,315540612828730,315655514736824,317661743264943,318803867724370,320714075796726,321798009185679,324151193665569,326396473229332,326807187700325,327138938126000,334796235238580,337189905171692,341543976606786,342351220395297,352489647219924,353275073777456,354028611831750,355805381525235,360747121114725,360868499205775,366644608904405,367982148237449,368093486690057,370098197696429,373928277594767,374705982436097,379375786576660,379655043896912,382261306625846,382348312579778,382652063634199,384084201228841,386614517514311,389387833053055,391112031499696,395705103820858,400997716674251,402847420318279,408260737941651,417075367308384,421077513177830,425574481908118,429691582829801,430660221592135,431231226411844,435016015312787,438631037334735,442764738248833,443945135300987,448224198777479,452010411958976,452153886582400,457295549871218,457972130788854,460455469757760,469997079185989,472209231076973,472874782213326,473353941468974,474353243832409,474475938845430,492518818251521,493944048707793,496808252451017,497807195735337,499795199148531,501928752291519,509362435555796,514504498255831,515496872941059,515574319545044,519536054211596,519903579658765,522156649215482,523539246039075,525686064099779,526530621305490,529026687214619,529186098184720,529477355884352,530151351540165,535614271802727,538002269773834,538750623047832,542136929689868,544840647719072,545125033161667,545142313363876,549088583109440,549128225213596,550722303250500,551793441391448,553557797867653,555395302972463,555823057496379,562106220544976,572437480369749,572734702293191,574919658191822,579402941474626,580257948489836,583877853606768,583941551650831,586705855499667,590774526969181,592577879096472,593999074744927,595733763100758,600128069807463,603787055170705,605634603212897,611437420775757,618772672842724,620898852233206,621820668444059,622456228655540,624066515917881,626457171905777,629062972432399,639401955254907,644117259872630,650392065241592,650861345898016,651273746578224,655512285528033,658316631039348,659409861906500,661044263974353,662985582550291,664349164558878,665676561527212,668473538877306,672545489461991,677686062373853,678508244316684,682452755537421,684552136839528,684640730665784,689007125469067,689313376792906,691170031635180,695081490699875,698502878633230,705170394113516,709448456048543,713814780180809,714005154320902,715589303254809,716022441992238,716530946963593,734984907093020,738300685269077,738802248944771,744347067914555,744725645864220,745136898699062,749329564936853,749473920066677,751782178017558,752280922694783,753519810978689,754411823049252,759014337068329,766804133841001,767795072682287,771491014999333,775786837419850,776263458865482,777142585286418,787162706630338,791695632613347,795312825337102,801816915302340,802864235221734,807222881500275,808888173144348,813570938107542,815581968941863,816859602935793,818551156177689,823176403547444,826241360947082,827968384357135,828775783347560,829956867192904,835917947876442,837513225315182,840523505643329,842326878000749,843441303039585,844386106384187,845942810173298,847233586025214,847266622926934,847915119416789,849889057512088,850714440636685,853343292758198,857780346940897,859636445864873,860091587639200,861595909381891,863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\ No newline at end of file
diff --git a/tests/test-data/sbt-search-bug/nano.sig b/tests/test-data/sbt-search-bug/nano.sig
new file mode 100644
index 000000000..9c1a88b09
--- /dev/null
+++ b/tests/test-data/sbt-search-bug/nano.sig
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/tests/test_sourmash.py b/tests/test_sourmash.py
index bf08b1b64..d223e52f2 100644
--- a/tests/test_sourmash.py
+++ b/tests/test_sourmash.py
@@ -1238,6 +1238,26 @@ def test_do_sourmash_sbt_search_output():
         assert 'short2.fa' in output
 
 
+# check against a bug in sbt search triggered by incorrect max Jaccard
+# calculation.
+def test_do_sourmash_sbt_search_check_bug():
+    with utils.TempDirectory() as location:
+        testdata1 = utils.get_test_data('sbt-search-bug/nano.sig')
+        testdata2 = utils.get_test_data('sbt-search-bug/bacteroides.sig')
+
+        status, out, err = utils.runscript('sourmash',
+                                           ['index', 'zzz', '-k', '31',
+                                            testdata1, testdata2],
+                                           in_directory=location)
+
+        assert os.path.exists(os.path.join(location, 'zzz.sbt.json'))
+
+        status, out, err = utils.runscript('sourmash',
+                                           ['search', testdata1, 'zzz'],
+                                           in_directory=location)
+        assert '1 matches:' in out
+
+
 def test_do_sourmash_sbt_move_and_search_output():
     with utils.TempDirectory() as location:
         testdata1 = utils.get_test_data('short.fa')
diff --git a/utils/check-tree.py b/utils/check-tree.py
new file mode 100644
index 000000000..15e16f1ed
--- /dev/null
+++ b/utils/check-tree.py
@@ -0,0 +1,32 @@
+#! /usr/bin/env python
+"""
+Check SBT search by taking every leaf node in a tree and checking to make
+sure we can find it.
+"""
+import argparse
+import sourmash
+from sourmash import sourmash_args
+from sourmash.sbtmh import search_minhashes
+
+THRESHOLD=0.08
+
+
+def main():
+    p = argparse.ArgumentParser()
+    p.add_argument('sbt')
+    args = p.parse_args()
+
+    db = sourmash.load_sbt_index(args.sbt)
+    threshold = THRESHOLD
+
+    for leaf in db.leaves():
+        query = leaf.data
+        matches = db.find(search_minhashes, query, threshold)
+        matches = list([ x.data for x in matches ])
+        if query not in matches:
+            print(query)
+            assert 0
+                                                 
+
+if __name__ == '__main__':
+    main()