diff --git a/R/XString-class.R b/R/XString-class.R
index 5e6333cc..1cb6bc66 100644
--- a/R/XString-class.R
+++ b/R/XString-class.R
@@ -434,6 +434,13 @@ setMethod("==", signature(e1="BString", e2="character"),
 setMethod("==", signature(e1="character", e2="BString"),
     function(e1, e2) e2 == e1
 )
+setMethod("==", signature(e1="XString", e2="character"),
+    ## Coerce to BString to handle things like RNAString("U") == "T"
+    function(e1, e2) as(e1, "BString") == e2
+)
+setMethod("==", signature(e1="character", e2="XString"),
+    function(e1, e2) e1 == as(e2, "BString")
+)
 
 setMethod("!=", signature(e1="XString", e2="XString"),
     function(e1, e2) !(e1 == e2)
@@ -444,7 +451,34 @@ setMethod("!=", signature(e1="BString", e2="character"),
 setMethod("!=", signature(e1="character", e2="BString"),
     function(e1, e2) !(e1 == e2)
 )
+setMethod("!=", signature(e1="XString", e2="character"),
+    function(e1, e2) as(e1, "BString") != e2
+)
+setMethod("!=", signature(e1="character", e2="XString"),
+    function(e1, e2) e1 != as(e2, "BString")
+)
 
+### Comparisons are already implemented for XStringSet objects,
+### so we can just dispatch to that code here.
+setMethod("<=", signature(e1="XString", e2="XString"),
+    function(e1, e2)
+    {
+        if (!comparable_seqtypes(seqtype(e1), seqtype(e2))) {
+            class1 <- class(e1)
+            class2 <- class(e2)
+            stop("comparison between a \"", class1, "\" instance ",
+                 "and a \"", class2, "\" instance ",
+                 "is not supported")
+        }
+        as(e1, "XStringSet") <= as(e2, "XStringSet")
+    }
+)
+setMethod("<=", signature(e1="XString", e2="character"),
+    function(e1, e2) as(e1, "BStringSet") <= e2
+)
+setMethod("<=", signature(e1="character", e2="XString"),
+    function(e1, e2) e1 <= as(e2, "BStringSet")
+)
 
 ### - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 ### The "substr" and "substring" methods.
diff --git a/tests/testthat/test-XString-class.R b/tests/testthat/test-XString-class.R
index 6253f758..0d18c2bf 100644
--- a/tests/testthat/test-XString-class.R
+++ b/tests/testthat/test-XString-class.R
@@ -137,14 +137,64 @@ test_that("equality methods work as advertised", {
     expect_true(AAString(aastr) != BString(bstr))
     expect_true(bstr == BString(bstr))
 
+    ## comparisons against character
+    expect_true(DNAString("AAA") == "AAA")
+    expect_true(DNAString("AAA") != "BBB")
+    expect_false(RNAString("UUU") == "TTT")
+    expect_true(AAString("UUU") == "UUU")
+    ## these may seem redundant but need to ensure that order doesn't matter
+    expect_true("AAA" == DNAString("AAA"))
+    expect_true("BBB" != DNAString("AAA"))
+    expect_false("TTT" == RNAString("UUU"))
+    expect_true("UUU" == AAString("UUU"))
+
+    ## invalid comparisons
+    expect_error(DNAString() == AAString(),
+      "comparison between a \"DNAString\" instance and a \"AAString\" instance is not supported")
+    expect_error(DNAString() == BString(),
+      "comparison between a \"DNAString\" instance and a \"BString\" instance is not supported")
+    expect_error(RNAString() == AAString(),
+      "comparison between a \"RNAString\" instance and a \"AAString\" instance is not supported")
+    expect_error(RNAString() == BString(),
+      "comparison between a \"RNAString\" instance and a \"BString\" instance is not supported")
+})
+
+test_that("inequality methods work as advertised", {
+    ## Basic cases
+    expect_true(DNAString("AAA") <= DNAString("AAAA"))
+    expect_false(DNAString("AAA") > DNAString("AAAA"))
+    expect_true(DNAString("AAA") <= DNAString("AAA"))
+    expect_true(DNAString("A") <= DNAString("C"))
+    expect_false(DNAString("ATTT") > RNAString("AUUU"))
+    expect_true(AAString("AAA") <= AAString("BBB"))
+    expect_true(BString("Testing") <= BString("ZZZTesting"))
+
+    ## have to check every combination for XString - character comparisons
+    ## due to how dispatch works
+    expect_true(BString("ABCDEFG") <= "ABCDEFG")
+    expect_true(BString("ABCDEFG") <  "ZYXWVUT")
+    expect_true(BString("ABCDEFG") >= "ABCDEFG")
+    expect_false(BString("ABCDEFG") > "ABCDEFG")
+
+    expect_true("ABCDEFG" <= BString("ABCDEFG"))
+    expect_false("ZYXWVUT" < BString("ABCDEFG"))
+    expect_true("ABCDEFG" >= BString("ABCDEFG"))
+    expect_false("ABCDEFG" > BString("ABCDEFG"))
+
+    ## Cases with potentially invalid characters
+    expect_true(DNAString("AAA") < "BBB")
+    expect_true(DNAString("CCC") > "BBB")
+    expect_true(RNAString("UUU") >= "TTT")
+    expect_true(RNAString("UUU") >= "UUU")
+
     ## invalid comparisons
-    expect_error(DNAString(dnastr) == AAString(aastr),
+    expect_error(DNAString() <= AAString(),
       "comparison between a \"DNAString\" instance and a \"AAString\" instance is not supported")
-    expect_error(DNAString(dnastr) == BString(bstr),
+    expect_error(DNAString() <= BString(),
       "comparison between a \"DNAString\" instance and a \"BString\" instance is not supported")
-    expect_error(RNAString(rnastr) == AAString(aastr),
+    expect_error(RNAString() <= AAString(),
       "comparison between a \"RNAString\" instance and a \"AAString\" instance is not supported")
-    expect_error(RNAString(rnastr) == BString(bstr),
+    expect_error(RNAString() <= BString(),
       "comparison between a \"RNAString\" instance and a \"BString\" instance is not supported")
 })