diff --git a/src/test/run-pass/tag-align-dyn-u64.rs b/src/test/run-pass/tag-align-dyn-u64.rs
index a50711fc98d..8d8d4caad24 100644
--- a/src/test/run-pass/tag-align-dyn-u64.rs
+++ b/src/test/run-pass/tag-align-dyn-u64.rs
@@ -8,9 +8,6 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-// ignore-linux #7340 fails on 32-bit Linux
-// ignore-macos #7340 fails on 32-bit macos
-
 use std::mem;
 
 enum Tag<A> {
@@ -26,12 +23,13 @@ fn mk_rec() -> Rec {
     return Rec { c8:0, t:Tag::Tag2(0) };
 }
 
-fn is_8_byte_aligned(u: &Tag<u64>) -> bool {
+fn is_u64_aligned(u: &Tag<u64>) -> bool {
     let p: uint = unsafe { mem::transmute(u) };
-    return (p & 7) == 0;
+    let u64_align = std::mem::min_align_of::<u64>();
+    return (p & (u64_align - 1)) == 0;
 }
 
 pub fn main() {
     let x = mk_rec();
-    assert!(is_8_byte_aligned(&x.t));
+    assert!(is_u64_aligned(&x.t));
 }
diff --git a/src/test/run-pass/tag-align-dyn-variants.rs b/src/test/run-pass/tag-align-dyn-variants.rs
index 69af882e1fa..917f2c5b374 100644
--- a/src/test/run-pass/tag-align-dyn-variants.rs
+++ b/src/test/run-pass/tag-align-dyn-variants.rs
@@ -8,9 +8,6 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-// ignore-linux #7340 fails on 32-bit Linux
-// ignore-macos #7340 fails on 32-bit macos
-
 use std::mem;
 
 enum Tag<A,B> {
@@ -42,33 +39,34 @@ fn variant_data_is_aligned<A,B>(amnt: uint, u: &Tag<A,B>) -> bool {
 }
 
 pub fn main() {
-    let x = mk_rec(22, 23);
-    assert!(is_aligned(8, &x.tA));
-    assert!(variant_data_is_aligned(8, &x.tA));
-    assert!(is_aligned(8, &x.tB));
-    assert!(variant_data_is_aligned(8, &x.tB));
+    let u64_align = std::mem::min_align_of::<u64>();
+    let x = mk_rec(22u64, 23u64);
+    assert!(is_aligned(u64_align, &x.tA));
+    assert!(variant_data_is_aligned(u64_align, &x.tA));
+    assert!(is_aligned(u64_align, &x.tB));
+    assert!(variant_data_is_aligned(u64_align, &x.tB));
 
-    let x = mk_rec(22, 23);
-    assert!(is_aligned(8, &x.tA));
-    assert!(variant_data_is_aligned(8, &x.tA));
-    assert!(is_aligned(8, &x.tB));
+    let x = mk_rec(22u64, 23u32);
+    assert!(is_aligned(u64_align, &x.tA));
+    assert!(variant_data_is_aligned(u64_align, &x.tA));
+    assert!(is_aligned(u64_align, &x.tB));
     assert!(variant_data_is_aligned(4, &x.tB));
 
-    let x = mk_rec(22, 23);
-    assert!(is_aligned(8, &x.tA));
+    let x = mk_rec(22u32, 23u64);
+    assert!(is_aligned(u64_align, &x.tA));
     assert!(variant_data_is_aligned(4, &x.tA));
-    assert!(is_aligned(8, &x.tB));
-    assert!(variant_data_is_aligned(8, &x.tB));
+    assert!(is_aligned(u64_align, &x.tB));
+    assert!(variant_data_is_aligned(u64_align, &x.tB));
 
-    let x = mk_rec(22, 23);
+    let x = mk_rec(22u32, 23u32);
     assert!(is_aligned(4, &x.tA));
     assert!(variant_data_is_aligned(4, &x.tA));
     assert!(is_aligned(4, &x.tB));
     assert!(variant_data_is_aligned(4, &x.tB));
 
     let x = mk_rec(22f64, 23f64);
-    assert!(is_aligned(8, &x.tA));
-    assert!(variant_data_is_aligned(8, &x.tA));
-    assert!(is_aligned(8, &x.tB));
-    assert!(variant_data_is_aligned(8, &x.tB));
+    assert!(is_aligned(u64_align, &x.tA));
+    assert!(variant_data_is_aligned(u64_align, &x.tA));
+    assert!(is_aligned(u64_align, &x.tB));
+    assert!(variant_data_is_aligned(u64_align, &x.tB));
 }
diff --git a/src/test/run-pass/tag-align-u64.rs b/src/test/run-pass/tag-align-u64.rs
index e5fd11ff9db..df99d77142c 100644
--- a/src/test/run-pass/tag-align-u64.rs
+++ b/src/test/run-pass/tag-align-u64.rs
@@ -8,9 +8,6 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-// ignore-linux #7340 fails on 32-bit Linux
-// ignore-macos #7340 fails on 32-bit macos
-
 use std::mem;
 
 enum Tag {
@@ -26,12 +23,13 @@ fn mk_rec() -> Rec {
     return Rec { c8:0, t:Tag::TagInner(0) };
 }
 
-fn is_8_byte_aligned(u: &Tag) -> bool {
+fn is_u64_aligned(u: &Tag) -> bool {
     let p: uint = unsafe { mem::transmute(u) };
-    return (p & 7) == 0;
+    let u64_align = std::mem::min_align_of::<u64>();
+    return (p & (u64_align - 1)) == 0;
 }
 
 pub fn main() {
     let x = mk_rec();
-    assert!(is_8_byte_aligned(&x.t));
+    assert!(is_u64_aligned(&x.t));
 }