diff --git a/lib/oga/xpath/parser.y b/lib/oga/xpath/parser.y
index 900679c..af8f440 100644
--- a/lib/oga/xpath/parser.y
+++ b/lib/oga/xpath/parser.y
@@ -6,12 +6,13 @@ class Oga::XPath::Parser
 token T_AXIS T_COLON T_COMMA T_FLOAT T_INT T_IDENT
 token T_LBRACK T_RBRACK T_LPAREN T_RPAREN T_SLASH T_STRING
 token T_PIPE T_AND T_OR T_ADD T_DIV T_MOD T_EQ T_NEQ T_LT T_GT T_LTE T_GTE
+token T_SUB T_MUL
 
 options no_result_var
 
 prechigh
-  left  T_EQ T_AXIS
-  right T_OR
+  left T_PIPE T_MOD T_DIV T_MUL T_SUB T_ADD
+  left T_GT T_GTE T_LT T_LTE T_NEQ T_EQ T_AND T_OR
 preclow
 
 rule
@@ -57,15 +58,32 @@ rule
     ;
 
   operator
-    : expression T_EQ expression { s(:eq, val[0], val[2]) }
-    | expression T_OR expression { s(:or, val[0], val[2]) }
+    : expression T_PIPE expression { s(:pipe, val[0], val[2]) }
+    | expression T_AND  expression { s(:and, val[0], val[2]) }
+    | expression T_OR   expression { s(:or, val[0], val[2]) }
+    | expression T_ADD  expression { s(:add, val[0], val[2]) }
+    | expression T_DIV  expression { s(:div, val[0], val[2]) }
+    | expression T_MOD  expression { s(:mod, val[0], val[2]) }
+    | expression T_EQ   expression { s(:eq, val[0], val[2]) }
+    | expression T_NEQ  expression { s(:neq, val[0], val[2]) }
+    | expression T_LT   expression { s(:lt, val[0], val[2]) }
+    | expression T_GT   expression { s(:gt, val[0], val[2]) }
+    | expression T_LTE  expression { s(:lte, val[0], val[2]) }
+    | expression T_GTE  expression { s(:gte, val[0], val[2]) }
+    | expression T_MUL  expression { s(:mul, val[0], val[2]) }
+    | expression T_SUB  expression { s(:sub, val[0], val[2]) }
     ;
 
   axis
-    : T_AXIS expression { s(:axis, val[0], val[1]) }
+    : T_AXIS axis_value { s(:axis, val[0], val[1]) }
     | T_AXIS            { s(:axis, val[0]) }
     ;
 
+  axis_value
+    : node_test
+    | call
+    ;
+
   call
     : T_IDENT T_LPAREN T_RPAREN           { s(:call, val[0]) }
     | T_IDENT T_LPAREN call_args T_RPAREN { s(:call, val[0], *val[2]) }
diff --git a/spec/oga/xpath/parser/operator_precedence_spec.rb b/spec/oga/xpath/parser/operator_precedence_spec.rb
new file mode 100644
index 0000000..69cd6ce
--- /dev/null
+++ b/spec/oga/xpath/parser/operator_precedence_spec.rb
@@ -0,0 +1,148 @@
+require 'spec_helper'
+
+describe Oga::XPath::Parser do
+  context 'operator precedence' do
+    example 'parse "A or B or C"' do
+      parse_xpath('A or B or C').should == s(
+        :path,
+        s(
+          :or,
+          s(:or, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+
+    example 'parse "A and B and C"' do
+      parse_xpath('A and B and C').should == s(
+        :path,
+        s(
+          :and,
+          s(:and, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+
+    example 'parse "A = B = C"' do
+      parse_xpath('A = B = C').should == s(
+        :path,
+        s(
+          :eq,
+          s(:eq, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+
+    example 'parse "A != B != C"' do
+      parse_xpath('A != B != C').should == s(
+        :path,
+        s(
+          :neq,
+          s(:neq, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+
+    example 'parse "A <= B <= C"' do
+      parse_xpath('A <= B <= C').should == s(
+        :path,
+        s(
+          :lte,
+          s(:lte, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+
+    example 'parse "A < B < C"' do
+      parse_xpath('A < B < C').should == s(
+        :path,
+        s(
+          :lt,
+          s(:lt, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+
+    example 'parse "A >= B >= C"' do
+      parse_xpath('A >= B >= C').should == s(
+        :path,
+        s(
+          :gte,
+          s(:gte, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+
+    example 'parse "A > B > C"' do
+      parse_xpath('A > B > C').should == s(
+        :path,
+        s(
+          :gt,
+          s(:gt, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+
+    example 'parse "A or B and C"' do
+      parse_xpath('A or B and C').should == s(
+        :path,
+        s(
+          :and,
+          s(:or, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+
+    example 'parse "A and B = C"' do
+      parse_xpath('A and B = C').should == s(
+        :path,
+        s(
+          :eq,
+          s(:and, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+
+    example 'parse "A = B < C"' do
+      parse_xpath('A = B < C').should == s(
+        :path,
+        s(
+          :lt,
+          s(:eq, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+
+    example 'parse "A < B | C"' do
+      parse_xpath('A < B | C').should == s(
+        :path,
+        s(
+          :lt,
+          s(:test, nil, 'A'),
+          s(:pipe, s(:test, nil, 'B'), s(:test, nil, 'C'))
+        )
+      )
+    end
+
+    example 'parse "A > B or C"' do
+      parse_xpath('A > B or C').should == s(
+        :path,
+        s(
+          :or,
+          s(:gt, s(:test, nil, 'A'), s(:test, nil, 'B')),
+          s(:test, nil, 'C')
+        )
+      )
+    end
+  end
+end
diff --git a/spec/oga/xpath/parser/operators_spec.rb b/spec/oga/xpath/parser/operators_spec.rb
new file mode 100644
index 0000000..4ec17bd
--- /dev/null
+++ b/spec/oga/xpath/parser/operators_spec.rb
@@ -0,0 +1,103 @@
+require 'spec_helper'
+
+describe Oga::XPath::Parser do
+  context 'operators' do
+    example 'parse the pipe operator' do
+      parse_xpath('A | B').should == s(
+        :path,
+        s(:pipe, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the and operator' do
+      parse_xpath('A and B').should == s(
+        :path,
+        s(:and, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the or operator' do
+      parse_xpath('A or B').should == s(
+        :path,
+        s(:or, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the plus operator' do
+      parse_xpath('A + B').should == s(
+        :path,
+        s(:add, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the div operator' do
+      parse_xpath('A div B').should == s(
+        :path,
+        s(:div, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the mod operator' do
+      parse_xpath('A mod B').should == s(
+        :path,
+        s(:mod, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the equals operator' do
+      parse_xpath('A = B').should == s(
+        :path,
+        s(:eq, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the not-equals operator' do
+      parse_xpath('A != B').should == s(
+        :path,
+        s(:neq, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the lower-than operator' do
+      parse_xpath('A < B').should == s(
+        :path,
+        s(:lt, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the greater-than operator' do
+      parse_xpath('A > B').should == s(
+        :path,
+        s(:gt, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the lower-or-equal operator' do
+      parse_xpath('A <= B').should == s(
+        :path,
+        s(:lte, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the greater-or-equal operator' do
+      parse_xpath('A >= B').should == s(
+        :path,
+        s(:gte, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the mul operator' do
+      parse_xpath('A * B').should == s(
+        :path,
+        s(:mul, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+
+    example 'parse the subtraction operator' do
+      parse_xpath('A - B').should == s(
+        :path,
+        s(:sub, s(:test, nil, 'A'), s(:test, nil, 'B'))
+      )
+    end
+  end
+end
diff --git a/spec/oga/xpath/parser/predicates_spec.rb b/spec/oga/xpath/parser/predicates_spec.rb
index ee1da97..1e0edf2 100644
--- a/spec/oga/xpath/parser/predicates_spec.rb
+++ b/spec/oga/xpath/parser/predicates_spec.rb
@@ -3,21 +3,18 @@ require 'spec_helper'
 describe Oga::XPath::Parser do
   context 'predicates' do
     example 'parse a single predicate' do
-      parse_xpath('/foo[@class="bar"]').should == s(
-        :absolute,
+      parse_xpath('foo[@class="bar"]').should == s(
+        :path,
         s(
-          :path,
+          :test,
+          nil,
+          'foo',
           s(
-            :test,
-            nil,
-            'foo',
+            :path,
             s(
-              :path,
-              s(
-                :eq,
-                s(:axis, 'attribute', s(:test, nil, 'class')),
-                s(:string, 'bar')
-              )
+              :eq,
+              s(:axis, 'attribute', s(:test, nil, 'class')),
+              s(:string, 'bar')
             )
           )
         )
@@ -25,28 +22,25 @@ describe Oga::XPath::Parser do
     end
 
     example 'parse a predicate using the or operator' do
-      parse_xpath('/foo[@class="bar" or @class="baz"]').should == s(
-        :absolute,
+      parse_xpath('foo[@class="bar" or @class="baz"]').should == s(
+        :path,
         s(
-          :path,
+          :test,
+          nil,
+          'foo',
           s(
-            :test,
-            nil,
-            'foo',
+            :path,
             s(
-              :path,
+              :or,
               s(
-                :or,
-                s(
-                  :eq,
-                  s(:axis, 'attribute', s(:test, nil, 'class')),
-                  s(:string, 'bar')
-                ),
-                s(
-                  :eq,
-                  s(:axis, 'attribute', s(:test, nil, 'class')),
-                  s(:string, 'baz')
-                )
+                :eq,
+                s(:axis, 'attribute', s(:test, nil, 'class')),
+                s(:string, 'bar')
+              ),
+              s(
+                :eq,
+                s(:axis, 'attribute', s(:test, nil, 'class')),
+                s(:string, 'baz')
               )
             )
           )