diff --git a/markdownify/__init__.py b/markdownify/__init__.py
index efb2d15..a37f870 100644
--- a/markdownify/__init__.py
+++ b/markdownify/__init__.py
@@ -7,7 +7,8 @@ import six
 convert_heading_re = re.compile(r'convert_h(\d+)')
 line_beginning_re = re.compile(r'^', re.MULTILINE)
 whitespace_re = re.compile(r'[\t ]+')
-all_whitespace_re = re.compile(r'[\s]+')
+all_whitespace_re = re.compile(r'[\t \r\n]+')
+newline_whitespace_re = re.compile(r'[\t \r\n]*[\r\n][\t \r\n]*')
 html_heading_re = re.compile(r'h[1-6]')
 
 
@@ -168,7 +169,11 @@ class MarkdownConverter(object):
 
         # normalize whitespace if we're not inside a preformatted element
         if not el.find_parent('pre'):
-            text = whitespace_re.sub(' ', text)
+            if self.options['wrap']:
+                text = all_whitespace_re.sub(' ', text)
+            else:
+                text = newline_whitespace_re.sub('\n', text)
+                text = whitespace_re.sub(' ', text)
 
         # escape special characters if we're not inside a preformatted or code element
         if not el.find_parent(['pre', 'code', 'kbd', 'samp']):
@@ -286,6 +291,7 @@ class MarkdownConverter(object):
         if style == UNDERLINED and n <= 2:
             line = '=' if n == 1 else '-'
             return self.underline(text, line)
+        text = all_whitespace_re.sub(' ', text)
         hashes = '#' * n
         if style == ATX_CLOSED:
             return '\n%s %s %s\n\n' % (hashes, text, hashes)
@@ -351,10 +357,21 @@ class MarkdownConverter(object):
         if convert_as_inline:
             return text
         if self.options['wrap']:
-            text = fill(text,
-                        width=self.options['wrap_width'],
-                        break_long_words=False,
-                        break_on_hyphens=False)
+            # Preserve newlines (and preceding whitespace) resulting
+            # from <br> tags.  Newlines in the input have already been
+            # replaced by spaces.
+            lines = text.split('\n')
+            new_lines = []
+            for line in lines:
+                line = line.lstrip()
+                line_no_trailing = line.rstrip()
+                trailing = line[len(line_no_trailing):]
+                line = fill(line,
+                            width=self.options['wrap_width'],
+                            break_long_words=False,
+                            break_on_hyphens=False)
+                new_lines.append(line + trailing)
+            text = '\n'.join(new_lines)
         return '\n\n%s\n\n' % text if text else ''
 
     def convert_pre(self, el, text, convert_as_inline):
diff --git a/tests/test_basic.py b/tests/test_basic.py
index bf25ee0..66f8b6c 100644
--- a/tests/test_basic.py
+++ b/tests/test_basic.py
@@ -11,3 +11,4 @@ def test_soup():
 
 def test_whitespace():
     assert md(' a  b \t\t c ') == ' a b c '
+    assert md(' a  b \n\n c ') == ' a b\nc '
diff --git a/tests/test_conversions.py b/tests/test_conversions.py
index baa294b..9c1edc3 100644
--- a/tests/test_conversions.py
+++ b/tests/test_conversions.py
@@ -1,4 +1,4 @@
-from markdownify import markdownify as md, ATX, ATX_CLOSED, BACKSLASH, UNDERSCORE
+from markdownify import markdownify as md, ATX, ATX_CLOSED, BACKSLASH, SPACES, UNDERSCORE
 
 
 def inline_tests(tag, markup):
@@ -113,6 +113,7 @@ def test_em():
 
 def test_header_with_space():
     assert md('<h3>\n\nHello</h3>') == '\n### Hello\n\n'
+    assert md('<h3>Hello\n\n\nWorld</h3>') == '\n### Hello World\n\n'
     assert md('<h4>\n\nHello</h4>') == '\n#### Hello\n\n'
     assert md('<h5>\n\nHello</h5>') == '\n##### Hello\n\n'
     assert md('<h5>\n\nHello\n\n</h5>') == '\n##### Hello\n\n'
@@ -174,7 +175,7 @@ def test_hn_nested_img():
         ("alt='Alt Text' title='Optional title'", "Alt Text", " \"Optional title\""),
     ]
     for image_attributes, markdown, title in image_attributes_to_markdown:
-        assert md('<h3>A <img src="/path/to/img.jpg" ' + image_attributes + '/> B</h3>') == '\n### A ' + markdown + ' B\n\n'
+        assert md('<h3>A <img src="/path/to/img.jpg" ' + image_attributes + '/> B</h3>') == '\n### A' + (' ' + markdown + ' ' if markdown else ' ') + 'B\n\n'
         assert md('<h3>A <img src="/path/to/img.jpg" ' + image_attributes + '/> B</h3>', keep_inline_images_in=['h3']) == '\n### A ![' + markdown + '](/path/to/img.jpg' + title + ') B\n\n'
 
 
@@ -214,10 +215,20 @@ def test_kbd():
 def test_p():
     assert md('<p>hello</p>') == '\n\nhello\n\n'
     assert md('<p>123456789 123456789</p>') == '\n\n123456789 123456789\n\n'
+    assert md('<p>123456789\n\n\n123456789</p>') == '\n\n123456789\n123456789\n\n'
+    assert md('<p>123456789\n\n\n123456789</p>', wrap=True, wrap_width=80) == '\n\n123456789 123456789\n\n'
     assert md('<p>123456789 123456789</p>', wrap=True, wrap_width=10) == '\n\n123456789\n123456789\n\n'
     assert md('<p><a href="https://example.com">Some long link</a></p>', wrap=True, wrap_width=10) == '\n\n[Some long\nlink](https://example.com)\n\n'
     assert md('<p>12345<br />67890</p>', wrap=True, wrap_width=10, newline_style=BACKSLASH) == '\n\n12345\\\n67890\n\n'
+    assert md('<p>12345<br />67890</p>', wrap=True, wrap_width=50, newline_style=BACKSLASH) == '\n\n12345\\\n67890\n\n'
+    assert md('<p>12345<br />67890</p>', wrap=True, wrap_width=10, newline_style=SPACES) == '\n\n12345  \n67890\n\n'
+    assert md('<p>12345<br />67890</p>', wrap=True, wrap_width=50, newline_style=SPACES) == '\n\n12345  \n67890\n\n'
     assert md('<p>12345678901<br />12345</p>', wrap=True, wrap_width=10, newline_style=BACKSLASH) == '\n\n12345678901\\\n12345\n\n'
+    assert md('<p>12345678901<br />12345</p>', wrap=True, wrap_width=50, newline_style=BACKSLASH) == '\n\n12345678901\\\n12345\n\n'
+    assert md('<p>12345678901<br />12345</p>', wrap=True, wrap_width=10, newline_style=SPACES) == '\n\n12345678901  \n12345\n\n'
+    assert md('<p>12345678901<br />12345</p>', wrap=True, wrap_width=50, newline_style=SPACES) == '\n\n12345678901  \n12345\n\n'
+    assert md('<p>1234 5678 9012<br />67890</p>', wrap=True, wrap_width=10, newline_style=BACKSLASH) == '\n\n1234 5678\n9012\\\n67890\n\n'
+    assert md('<p>1234 5678 9012<br />67890</p>', wrap=True, wrap_width=10, newline_style=SPACES) == '\n\n1234 5678\n9012  \n67890\n\n'
     assert md('First<p>Second</p><p>Third</p>Fourth') == 'First\n\nSecond\n\nThird\n\nFourth'
 
 
diff --git a/tests/test_tables.py b/tests/test_tables.py
index 594e5bf..fc6eee6 100644
--- a/tests/test_tables.py
+++ b/tests/test_tables.py
@@ -242,7 +242,7 @@ def test_table():
     assert md(table) == '\n\n| Firstname | Lastname | Age |\n| --- | --- | --- |\n| Jill | Smith | 50 |\n| Eve | Jackson | 94 |\n\n'
     assert md(table_with_html_content) == '\n\n| Firstname | Lastname | Age |\n| --- | --- | --- |\n| **Jill** | *Smith* | [50](#) |\n| Eve | Jackson | 94 |\n\n'
     assert md(table_with_paragraphs) == '\n\n| Firstname | Lastname | Age |\n| --- | --- | --- |\n| Jill | Smith | 50 |\n| Eve | Jackson | 94 |\n\n'
-    assert md(table_with_linebreaks) == '\n\n| Firstname | Lastname | Age |\n| --- | --- | --- |\n| Jill | Smith  Jackson | 50 |\n| Eve | Jackson  Smith | 94 |\n\n'
+    assert md(table_with_linebreaks) == '\n\n| Firstname | Lastname | Age |\n| --- | --- | --- |\n| Jill | Smith Jackson | 50 |\n| Eve | Jackson Smith | 94 |\n\n'
     assert md(table_with_header_column) == '\n\n| Firstname | Lastname | Age |\n| --- | --- | --- |\n| Jill | Smith | 50 |\n| Eve | Jackson | 94 |\n\n'
     assert md(table_head_body) == '\n\n| Firstname | Lastname | Age |\n| --- | --- | --- |\n| Jill | Smith | 50 |\n| Eve | Jackson | 94 |\n\n'
     assert md(table_head_body_missing_head) == '\n\n| Firstname | Lastname | Age |\n| --- | --- | --- |\n| Jill | Smith | 50 |\n| Eve | Jackson | 94 |\n\n'