diff --git a/CHANGELOG.md b/CHANGELOG.md
index 1ed8f89e244..c6a84910d08 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -46,6 +46,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
   ([#1818](https://github.com/open-telemetry/opentelemetry-python/pull/1818))
 - Update transient errors retry timeout and retryable status codes
   ([#1842](https://github.com/open-telemetry/opentelemetry-python/pull/1842))
+- Fix start span behavior when excess links and attributes are included
+  ([#1856](https://github.com/open-telemetry/opentelemetry-python/pull/1856))
 
 ### Removed
 - Moved `opentelemetry-instrumentation` to contrib repository.
diff --git a/opentelemetry-sdk/src/opentelemetry/sdk/util/__init__.py b/opentelemetry-sdk/src/opentelemetry/sdk/util/__init__.py
index 1bb8ed264fc..981368049fb 100644
--- a/opentelemetry-sdk/src/opentelemetry/sdk/util/__init__.py
+++ b/opentelemetry-sdk/src/opentelemetry/sdk/util/__init__.py
@@ -81,11 +81,8 @@ def extend(self, seq):
     @classmethod
     def from_seq(cls, maxlen, seq):
         seq = tuple(seq)
-        if len(seq) > maxlen:
-            raise ValueError
         bounded_list = cls(maxlen)
-        # pylint: disable=protected-access
-        bounded_list._dq = deque(seq, maxlen=maxlen)
+        bounded_list.extend(seq)
         return bounded_list
 
 
@@ -140,9 +137,7 @@ def __len__(self):
     @classmethod
     def from_map(cls, maxlen, mapping):
         mapping = OrderedDict(mapping)
-        if len(mapping) > maxlen:
-            raise ValueError
         bounded_dict = cls(maxlen)
-        # pylint: disable=protected-access
-        bounded_dict._dict = mapping
+        for key, value in mapping.items():
+            bounded_dict[key] = value
         return bounded_dict
diff --git a/opentelemetry-sdk/tests/test_util.py b/opentelemetry-sdk/tests/test_util.py
index cacc77dbd98..e003e70789c 100644
--- a/opentelemetry-sdk/tests/test_util.py
+++ b/opentelemetry-sdk/tests/test_util.py
@@ -61,8 +61,9 @@ def test_from_seq(self):
         self.assertEqual(len(tuple(blist)), list_len)
 
         # sequence too big
-        with self.assertRaises(ValueError):
-            BoundedList.from_seq(list_len / 2, self.base)
+        blist = BoundedList.from_seq(list_len // 2, base_copy)
+        self.assertEqual(len(blist), list_len // 2)
+        self.assertEqual(blist.dropped, list_len - (list_len // 2))
 
     def test_append_no_drop(self):
         """Append max capacity elements to the list without dropping elements."""
@@ -167,8 +168,10 @@ def test_from_map(self):
         self.assertEqual(len(tuple(bdict)), dic_len)
 
         # map too big
-        with self.assertRaises(ValueError):
-            BoundedDict.from_map(dic_len / 2, self.base)
+        half_len = dic_len // 2
+        bdict = BoundedDict.from_map(half_len, self.base)
+        self.assertEqual(len(tuple(bdict)), half_len)
+        self.assertEqual(bdict.dropped, dic_len - half_len)
 
     def test_bounded_dict(self):
         # create empty dict
diff --git a/opentelemetry-sdk/tests/trace/test_trace.py b/opentelemetry-sdk/tests/trace/test_trace.py
index e2e55bf9d08..236c604e879 100644
--- a/opentelemetry-sdk/tests/trace/test_trace.py
+++ b/opentelemetry-sdk/tests/trace/test_trace.py
@@ -21,8 +21,6 @@
 from typing import Optional
 from unittest import mock
 
-import pytest
-
 from opentelemetry import trace as trace_api
 from opentelemetry.context import Context
 from opentelemetry.sdk import resources, trace
@@ -538,6 +536,26 @@ def test_disallow_direct_span_creation(self):
             # pylint: disable=abstract-class-instantiated
             trace.Span("name", mock.Mock(spec=trace_api.SpanContext))
 
+    def test_surplus_span_links(self):
+        # pylint: disable=protected-access
+        max_links = trace._SPAN_LINK_COUNT_LIMIT
+        links = [
+            trace_api.Link(trace_api.SpanContext(0x1, idx, is_remote=False))
+            for idx in range(0, 16 + max_links)
+        ]
+        tracer = new_tracer()
+        with tracer.start_as_current_span("span", links=links) as root:
+            self.assertEqual(len(root.links), max_links)
+
+    def test_surplus_span_attributes(self):
+        max_attrs = trace.SPAN_ATTRIBUTE_COUNT_LIMIT
+        attributes = {str(idx): idx for idx in range(0, 16 + max_attrs)}
+        tracer = new_tracer()
+        with tracer.start_as_current_span(
+            "span", attributes=attributes
+        ) as root:
+            self.assertEqual(len(root.attributes), max_attrs)
+
 
 class TestSpan(unittest.TestCase):
     # pylint: disable=too-many-public-methods
@@ -1303,11 +1321,15 @@ def test_span_environment_limits(self):
             )
             for _ in range(100)
         ]
-        with pytest.raises(ValueError):
-            with tracer.start_as_current_span("root", links=some_links):
-                pass
 
-        with tracer.start_as_current_span("root") as root:
+        some_attrs = {
+            "init_attribute_{}".format(idx): idx for idx in range(100)
+        }
+        with tracer.start_as_current_span(
+            "root", links=some_links, attributes=some_attrs
+        ) as root:
+            self.assertEqual(len(root.links), 30)
+            self.assertEqual(len(root.attributes), 10)
             for idx in range(100):
                 root.set_attribute("my_attribute_{}".format(idx), 0)
                 root.add_event("my_event_{}".format(idx))