diff --git a/src/asm/section.cpp b/src/asm/section.cpp
index 43429b6a..8c6bc027 100644
--- a/src/asm/section.cpp
+++ b/src/asm/section.cpp
@@ -472,16 +472,15 @@ static Section *getSection(
 	if (alignment != 0) {
 		// It doesn't make sense to have both alignment and org set
 		if (org != UINT32_MAX) {
-			if ((org - alignOffset) & alignMask) {
+			if ((org & alignMask) != alignOffset) {
 				error("Section \"%s\"'s fixed address does not match its alignment", name.c_str());
 			}
 			alignment = 0; // Ignore it if it's satisfied
-		} else if (typeInfo.startAddr & alignMask) {
+		} else if ((typeInfo.startAddr & alignMask) > alignOffset) {
 			error(
 			    "Section \"%s\"'s alignment cannot be attained in %s", name.c_str(), typeInfo.name
 			);
 			alignment = 0; // Ignore it if it's unattainable
-			org = 0;
 		} else if (alignment == 16) {
 			// Treat an alignment of 16 as fixing the address.
 			alignment = 0;
diff --git a/src/link/section.cpp b/src/link/section.cpp
index b5de18d8..240d4341 100644
--- a/src/link/section.cpp
+++ b/src/link/section.cpp
@@ -258,7 +258,7 @@ static void doSanityChecks(Section &section) {
 	SectionTypeInfo const &typeInfo = section.typeInfo();
 
 	// Too large an alignment may not be satisfiable
-	if (section.isAlignFixed && (section.alignMask & typeInfo.startAddr)) {
+	if (section.isAlignFixed && (section.alignMask & typeInfo.startAddr) > section.alignOfs) {
 		error(
 		    "Section \"%s\" has type `%s`, which cannot be aligned to $%04x bytes",
 		    section.name.c_str(),
diff --git a/test/link/zero-byte-sect-constraints.asm b/test/link/zero-byte-sect-constraints.asm
index 4cd7d289..91ef762f 100644
--- a/test/link/zero-byte-sect-constraints.asm
+++ b/test/link/zero-byte-sect-constraints.asm
@@ -21,3 +21,7 @@ SECTION "free align16", ROM0, ALIGN[16,$2222] ; Should be equivalent to the abov
 
 SECTION "free align", ROM0, ALIGN[13,$1234] ; Has more than one suitable location, so cannot be trivially solved.
 	assert @ == $1234 ; Assuming that it goes into the first suitable location.
+
+
+SECTION "hram align", HRAM, ALIGN[8, $84]
+	assert @ == $FF84