diff --git a/packages/opentelemetry-tracing/src/Span.ts b/packages/opentelemetry-tracing/src/Span.ts
index 62d6f35e5f..6c21cf98a6 100644
--- a/packages/opentelemetry-tracing/src/Span.ts
+++ b/packages/opentelemetry-tracing/src/Span.ts
@@ -103,15 +103,10 @@ export class Span implements api.Span, ReadableSpan {
 
     if (
       Object.keys(this.attributes).length >=
-      this._traceParams.numberOfAttributesPerSpan!
+        this._traceParams.numberOfAttributesPerSpan! &&
+      !Object.prototype.hasOwnProperty.call(this.attributes, key)
     ) {
-      const attributeKeyToDelete = Object.keys(this.attributes).shift();
-      if (attributeKeyToDelete) {
-        this._logger.warn(
-          `Dropping extra attributes : ${attributeKeyToDelete}`
-        );
-        delete this.attributes[attributeKeyToDelete];
-      }
+      return this;
     }
     this.attributes[key] = value;
     return this;
diff --git a/packages/opentelemetry-tracing/test/Span.test.ts b/packages/opentelemetry-tracing/test/Span.test.ts
index 9bf0fb19fc..1b4819a43d 100644
--- a/packages/opentelemetry-tracing/test/Span.test.ts
+++ b/packages/opentelemetry-tracing/test/Span.test.ts
@@ -348,8 +348,9 @@ describe('Span', () => {
     assert.strictEqual(span.events.length, 100);
     assert.strictEqual(Object.keys(span.attributes).length, 100);
     assert.strictEqual(span.events[span.events.length - 1].name, 'sent149');
-    assert.strictEqual(span.attributes['foo0'], undefined);
-    assert.strictEqual(span.attributes['foo149'], 'bar149');
+    assert.strictEqual(span.attributes['foo0'], 'bar0');
+    assert.strictEqual(span.attributes['foo99'], 'bar99');
+    assert.strictEqual(span.attributes['sent100'], undefined);
   });
 
   it('should set an error status', () => {