diff --git a/Orange/data/domain.py b/Orange/data/domain.py
index 88e3245d819..3191e147646 100644
--- a/Orange/data/domain.py
+++ b/Orange/data/domain.py
@@ -11,6 +11,7 @@
 from Orange.data import (
     Unknown, Variable, ContinuousVariable, DiscreteVariable, StringVariable
 )
+from Orange.misc.cache import IDWeakrefCache
 from Orange.util import deprecated, OrangeDeprecationWarning
 
 __all__ = ["DomainConversion", "Domain"]
@@ -169,6 +170,7 @@ def __init__(self, attributes, class_vars=None, metas=None, source=None):
         self.anonymous = False
 
         self._hash = None  # cache for __hash__()
+        self._eq_cache = IDWeakrefCache(_LRS10Dict())  # cache for __eq__()
 
     def _ensure_indices(self):
         if self._indices is None:
@@ -185,6 +187,7 @@ def __setstate__(self, state):
         self._variables = self.attributes + self.class_vars
         self._indices = None
         self._hash = None
+        self._eq_cache = {}
 
     def __getstate__(self):
         # Do not pickle dictionaries because unpickling dictionaries that
@@ -195,6 +198,7 @@ def __getstate__(self):
         del state["_variables"]
         del state["_indices"]
         del state["_hash"]
+        del state["_eq_cache"]
         return state
 
     # noinspection PyPep8Naming
@@ -518,11 +522,26 @@ def __eq__(self, other):
         if not isinstance(other, Domain):
             return False
 
-        return (self.attributes == other.attributes and
-                self.class_vars == other.class_vars and
-                self.metas == other.metas)
+        try:
+            eq = self._eq_cache[(other,)]
+        except KeyError:
+            eq = (self.attributes == other.attributes and
+                  self.class_vars == other.class_vars and
+                  self.metas == other.metas)
+            self._eq_cache[(other,)] = eq
+
+        return eq
 
     def __hash__(self):
         if self._hash is None:
             self._hash = hash(self.attributes) ^ hash(self.class_vars) ^ hash(self.metas)
         return self._hash
+
+
+class _LRS10Dict(dict):
+    """ A small "least recently stored" (not LRU) dict """
+
+    def __setitem__(self, key, value):
+        if len(self) >= 10:
+            del self[next(iter(self))]
+        super().__setitem__(key, value)
diff --git a/Orange/data/table.py b/Orange/data/table.py
index c82f3e10271..c7f470a005a 100644
--- a/Orange/data/table.py
+++ b/Orange/data/table.py
@@ -29,6 +29,7 @@
 from Orange.data.util import SharedComputeValue, \
     assure_array_dense, assure_array_sparse, \
     assure_column_dense, assure_column_sparse, get_unique_names_duplicates
+from Orange.misc.cache import IDWeakrefCache
 from Orange.misc.collections import frozendict
 from Orange.statistics.util import bincount, countnans, contingency, \
     stats as fast_stats, sparse_has_implicit_zeros, sparse_count_implicit_zeros, \
@@ -305,10 +306,11 @@ def get_columns(self, source, row_indices, out=None, target_indices=None):
                 )
             elif not isinstance(col, Integral):
                 if isinstance(col, SharedComputeValue):
-                    shared = _idcache_restore(shared_cache, (col.compute_shared, source))
-                    if shared is None:
+                    try:
+                        shared = shared_cache[(col.compute_shared, source)]
+                    except KeyError:
                         shared = col.compute_shared(sourceri)
-                        _idcache_save(shared_cache, (col.compute_shared, source), shared)
+                        shared_cache[col.compute_shared, source] = shared
                     col_array = match_density(
                         _compute_column(col, sourceri, shared_data=shared))
                 else:
@@ -439,7 +441,7 @@ def convert(self, source, row_indices, clear_cache_after_part):
 
                 # clear cache after a part is done
                 if clear_cache_after_part:
-                    _thread_local.conversion_cache = {}
+                    _thread_local.conversion_cache.clear()
 
             for array_conv in self.columnwise:
                 res[array_conv.target] = \
@@ -805,12 +807,13 @@ def from_table(cls, domain, source, row_indices=...):
         new_cache = _thread_local.conversion_cache is None
         try:
             if new_cache:
-                _thread_local.conversion_cache = {}
-                _thread_local.domain_cache = {}
+                _thread_local.conversion_cache = IDWeakrefCache({})
+                _thread_local.domain_cache = IDWeakrefCache({})
             else:
-                cached = _idcache_restore(_thread_local.conversion_cache, (domain, source))
-                if cached is not None:
-                    return cached
+                try:
+                    return _thread_local.conversion_cache[(domain, source)]
+                except KeyError:
+                    pass
 
             # avoid boolean indices; also convert to slices if possible
             row_indices = _optimize_indices(row_indices, len(source))
@@ -818,12 +821,12 @@ def from_table(cls, domain, source, row_indices=...):
             self = cls()
             self.domain = domain
 
-            table_conversion = \
-                _idcache_restore(_thread_local.domain_cache, (domain, source.domain))
-            if table_conversion is None:
+            try:
+                table_conversion = \
+                    _thread_local.domain_cache[(domain, source.domain)]
+            except KeyError:
                 table_conversion = _FromTableConversion(source.domain, domain)
-                _idcache_save(_thread_local.domain_cache, (domain, source.domain),
-                              table_conversion)
+                _thread_local.domain_cache[(domain, source.domain)] = table_conversion
 
             # if an array can be a subarray of the input table, this needs to be done
             # on the whole table, because this avoids needless copies of contents
@@ -838,7 +841,7 @@ def from_table(cls, domain, source, row_indices=...):
                 self.attributes = getattr(source, 'attributes', {})
                 if new_cache:  # only deepcopy attributes for the outermost transformation
                     self.attributes = deepcopy(self.attributes)
-                _idcache_save(_thread_local.conversion_cache, (domain, source), self)
+                _thread_local.conversion_cache[(domain, source)] = self
             return self
         finally:
             if new_cache:
diff --git a/Orange/misc/cache.py b/Orange/misc/cache.py
index ee165934a3f..d813fba5d59 100644
--- a/Orange/misc/cache.py
+++ b/Orange/misc/cache.py
@@ -1,5 +1,6 @@
 """Common caching methods, using `lru_cache` sometimes has its downsides."""
 from functools import wraps, lru_cache
+from typing import MutableMapping
 import weakref
 
 
@@ -54,3 +55,31 @@ def _wrapped_func(self, *args, **kwargs):
         return _wrapped_func
 
     return _decorator
+
+
+class IDWeakrefCache:
+    """
+    Cache that caches keys according to their id() for speed. It also stores
+    weak references to the keys to ensure that the same keys are being accessed.
+    """
+
+    def __init__(self, cache: MutableMapping):
+        self._cache = cache
+
+    def __setitem__(self, keys, value):
+        self._cache[tuple(map(id, keys))] = \
+            value, [weakref.ref(k) for k in keys]
+
+    def __getitem__(self, keys):
+        key = tuple(map(id, keys))
+        if key not in self._cache:
+            raise KeyError()
+        shared, weakrefs = self._cache[key]
+        for r in weakrefs:
+            if r() is None:
+                del self._cache[key]
+                raise KeyError()
+        return shared
+
+    def clear(self):
+        self._cache.clear()
diff --git a/Orange/regression/tests/test_pls.py b/Orange/regression/tests/test_pls.py
index f289e6907c6..3b72e36e27a 100644
--- a/Orange/regression/tests/test_pls.py
+++ b/Orange/regression/tests/test_pls.py
@@ -124,6 +124,14 @@ def test_eq_hash(self):
         self.assertNotEqual(hash(proj1), hash(proj2))
         self.assertNotEqual(hash(proj1.domain), hash(proj2.domain))
 
+    def test_eq_hash_fake_same_model(self):
+        data = Table("housing")
+        pls1 = PLSRegressionLearner()(data)
+        pls2 = PLSRegressionLearner()(data)
+
+        proj1 = pls1.project(data)
+        proj2 = pls2.project(data)
+
         proj2.domain[0].compute_value.compute_shared.pls_model = \
             proj1.domain[0].compute_value.compute_shared.pls_model
         # reset hash caches because object were hacked
diff --git a/Orange/tests/test_domain.py b/Orange/tests/test_domain.py
index 368a50e6f2d..a5e32660a06 100644
--- a/Orange/tests/test_domain.py
+++ b/Orange/tests/test_domain.py
@@ -441,24 +441,74 @@ def test_different_domains_with_same_attributes_are_equal(self):
         self.assertEqual(domain1, domain2)
 
         var1 = ContinuousVariable('var1')
-        domain1.attributes = (var1,)
+        domain1 = Domain([var1])
         self.assertNotEqual(domain1, domain2)
 
-        domain2.attributes = (var1,)
+        domain2 = Domain([var1])
         self.assertEqual(domain1, domain2)
 
-        domain1.class_vars = (var1,)
+        var2 = ContinuousVariable('var2')
+        domain1 = Domain([var1], [var2])
         self.assertNotEqual(domain1, domain2)
 
-        domain2.class_vars = (var1,)
+        domain2 = Domain([var1], [var2])
         self.assertEqual(domain1, domain2)
 
-        domain1._metas = (var1,)
+        var3 = ContinuousVariable('var3')
+        domain1 = Domain([var1], [var2], [var3])
         self.assertNotEqual(domain1, domain2)
 
-        domain2._metas = (var1,)
+        domain2 = Domain([var1], [var2], [var3])
         self.assertEqual(domain1, domain2)
 
+    def test_eq_cached(self):
+
+        class ComputeValueEqOnce:
+            calls = 0
+
+            def __eq__(self, other):
+                if self.calls > 0:
+                    raise RuntimeError()
+                self.calls += 1
+                return type(self) is type(other)
+
+            def __hash__(self):
+                return hash(type(self))
+
+        var1 = ContinuousVariable('var1', compute_value=ComputeValueEqOnce())
+        var1a = ContinuousVariable('var1', compute_value=ComputeValueEqOnce())
+        domain1 = Domain([var1])
+        domain2 = Domain([var1a])
+        self.assertTrue(domain1 == domain2)
+
+        # the second call would crash if __eq__ was not cached
+        self.assertTrue(domain1 == domain2)
+
+        # modify the cache, see if that has an effect
+        domain1._eq_cache[(domain2,)] = False  # pylint: disable=protected-access
+        self.assertFalse(domain1 == domain2)
+
+    def test_eq_cache_not_grow(self):
+        var = ContinuousVariable('var')
+        domain = Domain([var])
+        domains = [Domain([var]) for _ in range(10)]
+        for d in domains:
+            self.assertTrue(domain == d)
+
+        # pylint: disable=protected-access,pointless-statement
+
+        # __eq__ results to all ten domains should be cached
+        for d in domains:
+            domain._eq_cache[(d,)]
+
+        dn = Domain([var])
+        self.assertTrue(domain == dn)
+        # the last compared domain should be cached
+        domain._eq_cache[(dn,)]
+        # but the first compared should be lost in cache
+        with self.assertRaises(KeyError):
+            domain._eq_cache[(domains[0],)]
+
     def test_domain_conversion_is_fast_enough(self):
         attrs = [ContinuousVariable("f%i" % i) for i in range(10000)]
         class_vars = [ContinuousVariable("c%i" % i) for i in range(10)]
diff --git a/Orange/tests/test_pca.py b/Orange/tests/test_pca.py
index e5f1c1d7283..ca59483a461 100644
--- a/Orange/tests/test_pca.py
+++ b/Orange/tests/test_pca.py
@@ -178,6 +178,12 @@ def test_eq_hash(self):
         self.assertNotEqual(hash(p1), hash(p2))
         self.assertNotEqual(hash(p1.domain), hash(p2.domain))
 
+    def test_eq_hash_fake_same_projection(self):
+        d = np.random.RandomState(0).rand(20, 20)
+        data = Table.from_numpy(None, d)
+        p1 = PCA()(data)
+        p2 = PCA()(data)
+
         # copy projection
         p2.domain[0].compute_value.compute_shared.projection = \
             p1.domain[0].compute_value.compute_shared.projection