diff --git a/src/liballoc/tests/heap.rs b/src/liballoc/tests/heap.rs
index c225ebfa96b91..904b3e7e1b07c 100644
--- a/src/liballoc/tests/heap.rs
+++ b/src/liballoc/tests/heap.rs
@@ -1,6 +1,6 @@
 use std::alloc::{Global, Alloc, Layout, System};
 
-/// Issue #45955.
+/// Issue #45955 and #62251.
 #[test]
 fn alloc_system_overaligned_request() {
     check_overalign_requests(System)
@@ -12,21 +12,23 @@ fn std_heap_overaligned_request() {
 }
 
 fn check_overalign_requests<T: Alloc>(mut allocator: T) {
-    let size = 8;
-    let align = 16; // greater than size
-    let iterations = 100;
-    unsafe {
-        let pointers: Vec<_> = (0..iterations).map(|_| {
-            allocator.alloc(Layout::from_size_align(size, align).unwrap()).unwrap()
-        }).collect();
-        for &ptr in &pointers {
-            assert_eq!((ptr.as_ptr() as usize) % align, 0,
-                       "Got a pointer less aligned than requested")
-        }
+    for &align in &[4, 8, 16, 32] { // less than and bigger than `MIN_ALIGN`
+        for &size in &[align/2, align-1] { // size less than alignment
+            let iterations = 128;
+            unsafe {
+                let pointers: Vec<_> = (0..iterations).map(|_| {
+                    allocator.alloc(Layout::from_size_align(size, align).unwrap()).unwrap()
+                }).collect();
+                for &ptr in &pointers {
+                    assert_eq!((ptr.as_ptr() as usize) % align, 0,
+                               "Got a pointer less aligned than requested")
+                }
 
-        // Clean up
-        for &ptr in &pointers {
-            allocator.dealloc(ptr, Layout::from_size_align(size, align).unwrap())
+                // Clean up
+                for &ptr in &pointers {
+                    allocator.dealloc(ptr, Layout::from_size_align(size, align).unwrap())
+                }
+            }
         }
     }
 }
diff --git a/src/libstd/sys/unix/alloc.rs b/src/libstd/sys/unix/alloc.rs
index 8e8f5017da75a..2c2dd3b77eae9 100644
--- a/src/libstd/sys/unix/alloc.rs
+++ b/src/libstd/sys/unix/alloc.rs
@@ -6,6 +6,10 @@ use crate::alloc::{GlobalAlloc, Layout, System};
 unsafe impl GlobalAlloc for System {
     #[inline]
     unsafe fn alloc(&self, layout: Layout) -> *mut u8 {
+        // jemalloc provides alignment less than MIN_ALIGN for small allocations.
+        // So only rely on MIN_ALIGN if size >= align.
+        // Also see <https://github.com/rust-lang/rust/issues/45955> and
+        // <https://github.com/rust-lang/rust/issues/62251#issuecomment-507580914>.
         if layout.align() <= MIN_ALIGN && layout.align() <= layout.size() {
             libc::malloc(layout.size()) as *mut u8
         } else {
@@ -21,6 +25,7 @@ unsafe impl GlobalAlloc for System {
 
     #[inline]
     unsafe fn alloc_zeroed(&self, layout: Layout) -> *mut u8 {
+        // See the comment above in `alloc` for why this check looks the way it does.
         if layout.align() <= MIN_ALIGN && layout.align() <= layout.size() {
             libc::calloc(layout.size(), 1) as *mut u8
         } else {
@@ -80,7 +85,10 @@ unsafe fn aligned_malloc(layout: &Layout) -> *mut u8 {
 #[inline]
 unsafe fn aligned_malloc(layout: &Layout) -> *mut u8 {
     let mut out = ptr::null_mut();
-    let ret = libc::posix_memalign(&mut out, layout.align(), layout.size());
+    // posix_memalign requires that the alignment be a multiple of `sizeof(void*)`.
+    // Since these are all powers of 2, we can just use max.
+    let align = layout.align().max(crate::mem::size_of::<usize>());
+    let ret = libc::posix_memalign(&mut out, align, layout.size());
     if ret != 0 {
         ptr::null_mut()
     } else {